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Squares and Square Roots Explained | Pre-Algebra Full Lesson
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May 1, 2025
In this lesson, we dive into squares, perfect squares, and square roots — essential building blocks for success in Algebra 1 and beyond! This beginner-friendly video breaks everything down in a clear, step-by-step way so you can master these key concepts. ✅ Key topics covered: What are perfect squares? How to recognize a perfect square number The definition of square roots (and how they relate to squares) Understanding the square root symbol and how to use it Estimating square roots of non-perfect squares Why you cannot take the square root of negative numbers (yet!) Introduction to simplifying square roots (early Algebra 2 sneak peek!)
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we are talking about square root Okay
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square root and perfect squares
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Something that you're going to talk
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about in algebra one with Mrs Hoffman if
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you take her class next year Whether you
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do algebra one honest or regular you're
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going to be meeting this You're going to
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be doing this Okay Yes I should bring in
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the little my
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Sure You bring whatever you want All
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right So we're going to talk about
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square and square root Okay Now here's
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the thing A number like four right four
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Four is a perfect square And why is it a
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perfect square because it's the square
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of an integer right meaning if I have
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four right four is equal to what you all
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know what's four 2 * 2 right 2 * 2
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meaning is
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2 right 2 * 2 is 2 square isn't it 2 * 2
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is the same as 2 square So because four
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is a product of two identical numbers
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two and two four is called a perfect
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square Why because 2 * 2 is equal to
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four So therefore we say that four is a
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perfect square Right
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if I draw four boxes then you make a
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square
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Yeah we can do that right You have
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multiple ways of like representing this
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What about give me an example of another
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perfect square What would be another
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perfect square nine Nine Why why is nine
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a perfect square because nine is what
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three * 3 So that's a perfect square
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right another one 64 64 Why is it
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perfect square 8 * 8 Right so anytime
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you have a number that can be broken
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down in two identical integers you call
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that number a perfect square Does that
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make sense so any even numbers or even
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numbers it doesn't matter There could be
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uneven like nine is an odd number It's
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still a perfect square because 9 is what
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3 * 3 So basically anytime you can break
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down no division on this 12 or division
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kind of right Anytime you can break down
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a number into two identical factors
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Therefore you have what you call a
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perfect square Does that make sense Does
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anybody have problem understanding the
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perfect square yes So the square the
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perfect square means you can divide that
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you can divide that one number in half
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Not half I wouldn't say half because
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nine is not divided by it's not half
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Anytime you can break down a number into
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two identical
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those two numbers together equal that
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the two numbers multiplied together
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equals that number Therefore you have a
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perfect square Yes All right So now
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here's the thing We have a perfect
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square We also have what you call the
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square root right square root And a lot
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of people uh it might be it might like
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look a little bit challenging but it's
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not It's really easy right so the
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opposite of a square is a square root So
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what is a square root by definition I'll
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give you the definition and then I will
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explain it A square root by definition
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is one A square root of a number is one
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of its equal factors Does anybody
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understand that a square root of a
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number is one of his equal factors does
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that make sense
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what does that mean anybody give me a
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definition beside you uh m what do you
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think that it of a number is one of his
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equal factors how would you explain that
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to someone that has never seen that
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before
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mhm
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You don't know YouTube video
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Anybody how would you explain that
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i don't know
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Anybody
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uh yeah How would you explain that
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square root of a number Can you Can you
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explain the voice wait Can I have a
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whiteboard marker hold on Yeah I have
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the camera on so I can't have you on the
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camera So sorry All right Let me explain
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it Right Let me explain what this means
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Right A square root a square root of a
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number is one of his equal five It mean
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it means that in other words what number
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multiplied by itself leads to that
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number right So what number one
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multiplied by itself leads to four three
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Two Two What number multiplied by itself
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leads to nine three What number
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multiplied by itself leads to 16 four
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Four So that's the square root of a
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number So the notation is a symbol is
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this here Right now I basically say now
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you are birthed into like higher math
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Right you've never seen this before and
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people write this and you go what is
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this whoa It's nothing It's square root
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Right so square root of four we say
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therefore is what two because square
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root of four is what number multiplied
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by itself twice gives you four two So
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square root of four will be two Yes you
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had your hand up So the definition is a
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number multiplied by itself is the
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number what what number multiplied by
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itself twice leads to the number that
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you are discussing In this case we did
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we said four So what number multiplied
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by itself gives you four two So
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therefore square root of four is two
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Right so now let me give you some
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example here We have a bunch on the
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board So what's square root of 9
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three Right so square root of 9 will be
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three What's root of 16
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four Now here this is also a little
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technical here I have plus or minus
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right so what's the square root of plus
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or minus 25 five If you plus or minus
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five right if you see the sign you keep
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it So you do plus or minus five right
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this is plus or minus 5 Okay What's the
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square root of 36 six right square root
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of 36 is 6 What is a negative root of 64
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what 8 Now I'm going try to see if you
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can figure this out What's the square
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root of 819
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can't be done Cannot be done You know
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why you cannot find the square root of a
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negative integer right but we can do
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complex numbers Who wants to do complex
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numbers no Now when you get to algebra
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one maybe you're going to talk about
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square root of 81 I squar right and that
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will be plus or minus 9 I So that's when
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you get to higher math right right now
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we're just going to be like anytime you
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have a square root of a negative number
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the answer will be
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cannot be what done because it's a
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negative number right so you cannot have
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a square root of a negative real number
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unless you use complex and we are not
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just using we not using complex numbers
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yet we're going to do that in algebra
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one So when you get there you going to
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remember what I said today right so now
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from now anytime you have a square root
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of a negative number you say it's
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impossible you can't do it but notice
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what if I did this negative square root
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of 81 what would that be then it would
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be9 right so make the distinction
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between this and that right this cannot
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be done this can be done Okay so that
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cannot be done but this can be done So
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that's a square root So now we're going
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to talk about how do you estimate the
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square root of a number that is not a
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perfect square So we going to talk about
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that too Okay I'm actually glad you guys
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are getting this Like I was thinking it
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was going to be hard but apparently
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everybody's getting it That's good Find
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the number Love it
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If we're getting it now
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uh nope
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Actually we're 24 hours away from
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Wednesday
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Actually a
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little less 16 hours Oh my god How many
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hours wait why is there a plus and minus
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time
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[Music]
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so let's say let me ask you a question
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All right So let's do something We're
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going to talk talk about estimating the
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square root of a non-perfect square
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right so what if I wanted to find the
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square root of 33
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what do you think is challenging while
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it's here square root of
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33 Just tell me what square It's not a
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perfect square Pay attention here Hey
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hey hey hey pay attention here You need
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to pay attention right square root of 33
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The first thing you see is this 33 is
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not a
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perfect
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square right it's not a perfect square
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So how would you estimate it so what
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would you do
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here what would you do do something to
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it to make it We can't make it perfect
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but we can find some numbers that 33 is
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in between Yes use decimals We can use
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decimals right we can use our
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calculators but we're going to use we're
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going to try to see if we can estimate
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it right so we can say that what is the
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closest square to 33 on both sides
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either less or more Yeah Wait but Mr
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Swami can we just do 11 square root of
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three i mean no the power of three No no
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no you can't Cuz 33 cannot be broken
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down into two equal numbers right can he
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no Right But find two numbers that are
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enclosed in 33 that are closer to 33 on
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the lower side and the higher side
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What's the closest perfect square to 33
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on the lower side 32 No 30 No Keep
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thinking 25 25 25 Right And what's the
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closest perfect square of 33 on the
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higher side 36 36 right So therefore we
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know that square root of 33 will be what
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it will be
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between square root of 25 and of 36 The
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value will be somewhere in between those
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two Right square root of 36 we know that
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is what 6 And square root of 25 is 5 So
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therefore root of 33 we say that it's
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it's going to be anywhere between what
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five and six Five and six But it's going
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to be closer to six because 33 is to 36
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So that's is how you estimate it Right
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now to be more precise we just have to
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use our calculator Just put of 33 If you
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have a calculator you have 5.7 You can
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just put in your calculator and that's
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easy Right Okay So that's how you do You
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just use your calculator and just plug
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it in and it's going to give you 1.7
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Start with estimating So what did you
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get for square to 33 on the calculator
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5.7 mm 44 44 56 56 26 26 So you see it's
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closer to what six So our estimate was
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pretty good We are closer to six than we
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are to five right but you can use your
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calculator I just wanted to show you how
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you do it If you don't have a calculator
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you can estimate You say "Well it's
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somewhere between five and six." But
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he's closer to six than it is to five
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because 33 is closer to six Okay All
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right So now we're going to work on a
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word problem which you guys love a lot
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right word problems Who loves word
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problems
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i hate word problems Problems can be
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useful So actually it depends on what
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we're learning So sometimes math word
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problems are easy sometimes they're not
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Peppa's house What
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i made a 3D model of Peppa's house
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All right So going forward in this
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chapter if we have a problem that we
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want to solve and the number that we are
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looking to work with is not a perfect
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square I suggest you use your calculator
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to find the square root of that number
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Right if it's not a perfect square if it
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is a perfect square first try to see if
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it's a perfect square If it's not then
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use your calculator right otherwise do
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it by hand cuz you can figure it out
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Okay in uh in car I want to show you
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something real quick but we're not going
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to learn it today because you guys it's
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going to be in algebra one probably I
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want to show you something okay so uh
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for example if I want to find square
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root of 27 there's a way to write square
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of 27 is 27 a perfect square no right 27
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is not a perfect square but 27 can be
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written as a perfect as a combination of
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a number and a perfect square can it yes
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or no yes right so 27 is what 3
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and 9 right 3 * 9 is 27 isn't it Right
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So here's what we do in algebra 2 right
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in 2 I'll show you something that maybe
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if you want to learn it you can learn it
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but you don't have to learn it now right
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so we're going to we're going to break
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down 27 It's going to be what square
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root of 9 * what square root of three
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right cuz 27 we can write break it down
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into square root of 9 * of 3 can't we
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yes Right now we know what's of 9 Three
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So this becomes what 3 square root of
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three So this is what we do in two We
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learn how to simplify the square root of
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a number Right Okay So in number two we
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do that But we're not going to do this
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here Unless you guys really want to
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learn it I can teach it to you I want to
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do it You guys want to do it show me and
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you guys want to do it But you don't
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know how to do it All right So let's do
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one more question
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Why is it three on the outside what why
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is there three on the outside why is it
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three on the outside because because
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square root of nine is three right
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that's why So let's do one more just to
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learn it and then we can end it right
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what about square root of 56 what am I
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going to do here 56
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[Music]
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Eight and seven right eight and seven
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And then eight is what
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four and two right seven is just seven
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right so now we going to break down the
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six into what square root of four right
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time square root of what 2 * square
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of 7 Seven right do we know of four two
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Two right so now becomes this becomes
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what 2 * 7 is 14 So therefore of 56 is
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two square root of 14 Right so you guys
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going to do that But the problem is with
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this number is really easy What if you
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have a huge number right so it's really
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easy So because it's just complex So
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what if you have,24
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you need to calculate Okay you want to
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do it So we want to break it down right
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we break it down and we can get it down
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too We can break it down and get it down
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So this is how we how we simplify square
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root in algebra 2 We don't use decimal
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numbers We actually simplify it All
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right All right So this is it for this
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chapter It has a little packet