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In today's lecture we'll quickly learn how to find the square of a number and find the square root of a number.
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this is thaiba taves.com or hasakix.com
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and today we're going to learn some
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basic
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uh concepts in algebra one okay so i've
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been touring for over 20 years
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and i've seen that a lot of people
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especially high school
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and middle middle school and even
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college students struggle with like
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terminologies like
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when when usually they are given a
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problem they don't know what to do
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and that's because i don't know if they
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just
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were never thought like uh this is what
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this means but today what i want to do
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is i want to teach just the basic
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concepts and and the first thing that
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we're going to start with is like square
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and square root okay so if you see on my
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board
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i said something here how do you find
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the square
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of a number so example if i ask you
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what is 3 squared what am i asking you
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to do
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if you don't understand the definition
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it's hard for you to do the problem
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so when i say how do you find the square
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of a number
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or if i ask you to find a square of a
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number what i'm
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actually saying to you is this multiply
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that number by itself
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so if i say what is 3 squared and i'm
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going to write that on the board
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what is
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3 squared
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so i'm technically saying to you
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multiply
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3 by itself so 3 squared is written
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3 to the power of 2 like this this is
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the notation
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and 3 squared is 3 times 3 and that
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gives you
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9. so if you have someone say what is
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3 squared or what is 4 squared they are
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basically saying to you
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what is 4 times 4 so squaring a number
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is basically taking that number and
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multiplying that number
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by itself so 5 squared will be 25
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because 5 times 5 is 25
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and because 5 squared is 5 times 5. so 6
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squared is six times six so if i if you
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hear someone say
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what is the square root of ten is ten
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times ten it's a hundred
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so don't be uh well what's the term like
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flabbergasted don't be so surprised this
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is this is simple stuff once you
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understand the terminology
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it gets easier now we're going to jump
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into something more complicated
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now if i say complicated no because it's
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too hard it's because people make it
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complicated
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so now we're going to talk about square
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root okay
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square root so let's say
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let's find
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the square root
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square root of uh
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let's say 16. so the first thing you
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need to understand is
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what am i asking you when i say find the
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square root of 16 what am i saying
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so what i'm saying to you is this what
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number
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multiplied by itself gives you 16.
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and those numbers are called perfect
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squares
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okay so 16 is a perfect square why i'm
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going to explain it
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so what number multiplied by itself
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gives you 16 is 4 because 4 times 4 is
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16.
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so square root of 16 is written this way
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it's like a v
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okay square root of 16 and square root
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of 16 is
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4 because
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4 times 4 gives you
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16. so basically when you hear what is
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the square root of a number
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what they are asking you is what number
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multiplied by itself
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gives you that original number that you
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are asked to find
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the per the square root off so in this
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case if i say what is the square root of
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25
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it will be 5 because 5 times 5
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is 25 what is the square root of 100 it
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would be 10 because 10
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times 10 is equal to 100 what is the
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square root of 169
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is 13 because 13 times 13 is 169.
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now a quick pointer so with square root
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what you need to remember is your times
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table
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okay when we were younger i had to learn
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my time still when i was like seven or
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eight or nine or
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out of learning so once you know your
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time stable these get so easy
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because once you know your time stable
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you can kind of figure out the numbers
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that you have been given
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so if i give you for example square root
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of um
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81 is 9 because i know that 9 times 9 is
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81
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okay that's because i learned my times
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table what is square root of 144
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is 12 because 12 times 12 is 144.
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now that you understand what the square
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root is uh
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i also explained the perfect square a
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perfect
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square is a number that multiplied by
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itself
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gives you the original number in this
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case 9 is a perfect square because
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3 times 3 is equal to 9. 25 is a perfect
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square
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because 5 times 5 is 25.
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now let's learn some basic rules when it
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comes to square roots
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rule number one we are dealing with
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real numbers okay with real numbers you
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cannot find the square root of
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a negative number for example square
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root of negative 7
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that will not exist you can't have that
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because you can't have the square root
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of a negative number
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now when you go on and deal with complex
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numbers
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that can be done but with real numbers
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you cannot
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okay so square root of negative seven
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you can't find it but if you were
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dealing with
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complex numbers square root of negative
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seven will be square root of seven
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i squared and we're gonna see that maybe
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in later chapters but now
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we are not gonna deal with complex
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numbers so don't even bother with it
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square root of negative seven does not
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exist as far as
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real numbers are concerned now this is
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just one thing that i wanted to point
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out
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now another thing you need to know some
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basic rules with square root
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so square root of a times
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b is the same as saying square root of a
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times square root of b okay and then
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square root of a
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divided by b is the same as saying
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square root of a
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divided by square root of b now square
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root of
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a plus b is not
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equal to square root of a plus square
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root of b
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and then square root of a minus b is
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not equal to square root of a minus
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square root of b
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this is not equal but as fast as
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multiplication any division are
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concerned yes
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but with the multiplication with the
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addition and subtraction
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you cannot do that this is not the same
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you just need to remember this you can
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take a screenshot at it
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you can do whatever you want but just
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remember that now let's do some
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quick problems now
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if i ask you to find square root of 5
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can you do it probably no why
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because there's no number that
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multiplied by itself
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gives you 5. there's no such a number
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there's not such a number not in this
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side of eternity
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maybe later on but now we can't find
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square root of five it's going to give
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you two point something something
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something
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so this is not a perfect square so we
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can't find
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square root of five okay now what about
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square root of uh
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16 we've already talked about it if you
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know your times table you know that
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square root of 16
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is what four all right now let's let's
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let's find like a more complex number
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let's say i wanted you i wanted you to
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find square root of 18.
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now what i'm asking you is this is there
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a number that multiplied by itself
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gives you 18 no but we can still
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simplify this
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because what 18 can be written as what
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times 9 and 18 is also what
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6 times 3 now here's the thing when you
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break it down into 2 times 9
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guess what 9 is a perfect square so i
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can do something here
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we just learn a couple of rules and
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we're going to apply those rules because
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they're going to help us
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the square root of 18 is what 2 times 9
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and we said earlier that square root of
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a b
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is the same as saying square root of a
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times square root of b
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so this can be written as square root of
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nine
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times square root of two now i know
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square root of nine
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square root of nine is three because
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what number
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multiplied by itself gives you nine is
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three so this gives you
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three square root of two because square
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root of two
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you can't find the square root of two
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it's not a perfect square so we stop
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right there okay now let's let's find
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another
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number that's a little more difficult
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let's find
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the square root of 108
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okay 108 so what do we do with 108
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so 108 the first thing you want to do is
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you want to break down 108 into small
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factors okay
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simpler factors and what my goal is to
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find a perfect square when i do this
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the breakdown so 108 can be written as
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what
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oh quick thing now how do you find the
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factors of one or eight
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you can kind of cheat because look 108
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he ends with
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eight eight is a multiple of what two so
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therefore this number
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can be divided by two so when i divide
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one or eight by two i get 54.
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once again 54 54
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ends with four so therefore i can divide
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it by two because four is a multiple of
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two so that gives you what two and
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twenty seven
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not twenty seven if you knew your times
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table you know that three times nine is
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twenty seven
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now what if you didn't know your times
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table what do you do
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look 27 you see the digits in 27
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2 plus 7 2 plus 7 is what 9
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2 plus 7 is 9 and 9 is a multiple of 3
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so therefore 9 27 can be divided by 3.
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so if when i divide it i get what 3 and
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9 and look here
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so we broke down 108 into 2 times 2
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times 3 times 9.
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9 is a perfect square so therefore we
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can rewrite this whole
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expression so square root of 108
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will be equal to square root of what two
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times two
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times nine times three now look two
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times two
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i'm gonna do something here i get square
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root of what four
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times nine times three okay
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now this is going to be easy because
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guess what we know we can break this
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down into what square root of 4
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times square root of 9 times square root
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of
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3 because we just learned our rule
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earlier right
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square root of 4 is what 2 square root
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of 9 is 3
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square root of 3 stays the same because
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this is not a perfect square
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and the final answer is 6 square root of
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3. all right so square root of 108
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can be simplified as 6 square root of 3
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by using this easy method you just break
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down the
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the number into small factors and try to
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see if you can find some perfect
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squares in there and that can help you
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better all right
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so to recap what we talked about today
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the first thing we talked about is
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uh how to find this the square of a
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number so if i say to you
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what is 5 squared i'm basically asking
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you
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multiply 5 by itself so squaring a
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number is basically
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multiplying that number by itself all
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right
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and the next thing we also talked about
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is how do you find the squared
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root of a number so to find the square
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root of a number is basically saying
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what number multiplied by itself gives
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you the original number so if i say find
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the square root of nine
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i'm basically asking you what number
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multiplied by itself
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gives you nine and it's three all right
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so right so we're going to wrap this up
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so i hope you enjoyed
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this quick uh intro to squaring a number
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and finding the square root of a number
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now if you are struggling with algebra
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one
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two finite mathematics statistics
11:40
calculus one calculus through
11:41
trigonometry or whatever you're
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struggling with
11:44
if you need a tutor i'm here to help
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please reach out i'll have a link for
11:48
you in my description
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check that out and you can schedule an
11:51
appointment we can work through google
11:52
meet or
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zoom whatever is to your liking all
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right again thanks for watching this is
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tyree from house of kicks and ty from
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types.com
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stay tuned for more quick videos in
12:02
mathematics thank you
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