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How to Quickly Solve Radical Equations
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Feb 19, 2025
In this video, we'll learn how to solve radical equations. If you need tutoring help, don't hesitate to contact me at https://dothatmath.com/
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0:01
so in this particular lecture this is
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for Algebra 2 Algebra 2 regular and on
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so we're going to learn how to solve
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veral equations and inequalities our
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first session will be just uh regular
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equations without the uh inequalities
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all right so these are pretty much we
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have three classic cases here so I gave
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you the first cases when you are solving
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an equation there's a square root with
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one radical in the equation first one
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has one radical in the equation the
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second one has two radicals and then the
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third one is a cubic uh equation now the
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thing is is once you understand thej of
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it I don't care what I put here I can
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put a cubic equation a fourth degree
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equation 50 you can solve it it's the
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same process all right so uh so what I'm
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going to do here is I'm going to show
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you how to solve this equation it's
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pretty simple simple stuffff I'm trying
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to find by a blue marker
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I guess I don't have one I don't know
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where it went anyway I'm going to keep
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it I'm going to use the black one all
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right so the first thing you want to do
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here is you want to
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isolate uh the you want to make sure the
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radical is by itself and the numbers on
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one side okay you want to isolate them
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so basically we going to subtract four
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on both side of the equation so now we
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have x + 2 = 3 now you can solve this
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equation the rest of the process is
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really simple so I want to get rid of
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radical okay the previous chapter we
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talked about how to do that right so
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this is a square root which is I can
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kind of turn into x + 2^ 12 all right =
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3 I'm going to show you what actually
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happens so basically you trying to get
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rid of the exponent so to get rid of the
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exponent 1/2 you need to multiply the
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1/2 by what two or you need to raise
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this to the power of two but if you do
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one thing on one side of the equation
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you have to repeat this process on the
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other side so this is basically this
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Square all right you squaring this all
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right so when that happens this
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eliminate the exponent so you're left
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with just x + 2 because 1 12 * 2 which
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is 1 and then 3 S is 9 and now you just
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have a regular equation that you can
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solve by just subtracting two on both
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side of the equation so you subtract two
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subtract two you get x = 7 and you have
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pretty much done now you can always
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double check to make sure this is right
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so you can take this seven and BR it
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into the equation to see if you going to
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get the same result so if you do of 7 +
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2 that's of 9 which is 3 3 + 4 is seven
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so yes you checked it this works you're
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good to go the next is now you have
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square root equation with two vares okay
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two vles so you have verticle here and a
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vertical here so they already isolated
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so this is on this side this is on this
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side so all you have to do is square
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both Sid of the equations here you going
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to square both side
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okay when that happens again this
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eliminate the radical so you are left
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with x - 2 12 we saw that on the last
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problem okay and now here you're going
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to have to do the finding method right
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so you're going to you can go the
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traditional way which is this time this
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so that way you run into TR okay so this
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is x - 12 2 and 2 that's 4 2 and this is
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--2k
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xkx * 2 this is -2
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xun x * otk X isun x² which isett pretty
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much absolute value of x or for the sake
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of considering that these are positive
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we going to leave it at X okay so this
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is x - 12 = 4 - 4un x - x all right so
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now what you want to do is you want to
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repeat the process that you did here so
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you want to put all the variables
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without the vertical on one side so I'm
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going to keep this on this side I'm
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going to move everything that's on the
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other side okay so I'm going to subtract
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the four here and I'm going to add an X
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and I'm going to do the same thing here
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subtract four from this guy because this
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is going to cancel out and then I add X
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here so I get 2x - 16 = to
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-4 x and now to solve this I'm going to
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square both Sid again cuz I want to get
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the Val right I'm going to square both
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Sid so I'm going to go like this I'm
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going to go like that so that gives me
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2x - 16 2 = -4k x² that is 16 x okay you
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already know how to do that4 * 4 is 16 x
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* X is just X and now we have to for
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this guy okay again I'm not going to I'm
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going to have to go and do this step by
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step oh my gosh my eyes something wrong
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with my eyes right now
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s anyway uh oh I run you into a big
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Problem by
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teacher we got a little problem here I
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just realized what I did I made a
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mistake also okay * negative is a
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positive so we should have a posi X so
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we Chang the whole dynamical equation so
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we have that = 4 - 4 x + x it happens to
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the best of us right so I'm going to
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subtract four here subtract the next
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subtract the next here subtract the four
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this cancels out we get -16 right equals
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to uh -4x all right so again you can
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divide this by4 both side you have
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multiple options here so you get 4 =
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rootx and then solve it again we get the
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same that we going to do here I want to
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get squ of X so I'm going to square both
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side right so you get 16 is equal to X
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and again you can double check make sure
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this is the right answer so you're going
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to plug in 16 here 16 - 12 that's 4
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which is 2
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plug in 16 here this is U uh 2 - uh < TK
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of 16 is 4 2 - 4 is -2 so we got a
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little problem so this is not a good
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solution I don't know what that is I
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don't know what I did wrong did I did
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something wrong here
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probably no I no so there's no solution
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to this problem so basically because
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when you plug in 6 here you get a 16 - 2
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that is 16 -
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of 4 which is 2 and if you plug into 16
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here you get
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2-k 16 which is -2 so there's no
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solution to this problem this problem
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has no solution all
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right again now the last one is a cubic
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function again it's the same process
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we're going to isolate the numbers okay
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so I'm going to add four
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here so I get 2 * 6x - 3 1/3 = 4 / 2
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we get 6 x - 3
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1/3 = 2 and now again if I want to get
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rid of the Cub root I need to raise it
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to the^ of three because this is 1/3
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right and remember you do one thing on
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one side you have to repat it on the
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other side so this cancel this out so
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you're left 6 6 x - 3 = 8 Out 3 Out 3
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you get 6 x 11 and then X
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is 11 / 6 now plug plug it in and double
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check to make sure your answers are
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right now so this process is really
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simple all right so again you just have
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to make sure you isolating first case
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you isolate the radical numbers of one
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side radical on the other side because a
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square root you square it to get rid of
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the r here you have two radical separate
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them Square them and solve the process
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so using this process and the last one
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again this a cubic R you want to isolate
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the game the radicle and the and then
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because a cubic root you raise it to the
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power three if it's a fourth root raise
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it to the four it's a fifth root raise
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it to the five say 10 fruit raise it to
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the 10 so the same process for each one
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of them all right so I hope this helps
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out uh see you next time