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substraction/addition inside square roots

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substraction/addition inside square roots [#permalink]

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New post 08 Nov 2017, 17:25
From my understanding square root (36^2 + 15^2) is not 36+15, you'd need to find the GCF and it'd end up being square root of ((3^2 (144+25))

There is a veritas prep question that says if x not equal to 0, and x=square root (4xy-4y^2) then in terms of y, x=
and it basically says to solve you'd square both sides first, then turn it into a quadratic equation
so my question is why are you allowed to square the 4xy-4y^2?

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Re: substraction/addition inside square roots [#permalink]

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New post 08 Nov 2017, 18:16
jasonfodor wrote:
From my understanding square root (36^2 + 15^2) is not 36+15, you'd need to find the GCF and it'd end up being square root of ((3^2 (144+25))

There is a veritas prep question that says if x not equal to 0, and x=square root (4xy-4y^2) then in terms of y, x=
and it basically says to solve you'd square both sides first, then turn it into a quadratic equation
so my question is why are you allowed to square the 4xy-4y^2?


nevermind, I think when solving for a value you can't take the square root
but if you are solving for a variable you can square both sides

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Re: substraction/addition inside square roots [#permalink]

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New post 08 Nov 2017, 18:47
you can add and subtract as long as the exponents are outside of the parenthesis ex: (36+15)^2
but you can't do so when you have exponents for each of them. Best approach, find the common factors for both of the terms, then bring it up front, in this case, 3^2.
in second case, 4y.

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Re: substraction/addition inside square roots [#permalink]

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New post 13 Nov 2017, 12:52
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jasonfodor wrote:
From my understanding square root (36^2 + 15^2) is not 36+15, you'd need to find the GCF and it'd end up being square root of ((3^2 (144+25))

There is a veritas prep question that says if x not equal to 0, and x=square root (4xy-4y^2) then in terms of y, x=
and it basically says to solve you'd square both sides first, then turn it into a quadratic equation
so my question is why are you allowed to square the 4xy-4y^2?


Good question!

The rule is: you can't split or join square roots (when doing addition or subtraction.)

For example,\(\sqrt{9}+\sqrt{16}\) is not equal to \(\sqrt{25}\), even though 9 + 16 = 25.

It's also true with variables: \(\sqrt{x} + \sqrt{y}\) is not equal to \(\sqrt{x+y}\). The only exception is when x or y is equal to 0.

In the Veritas question, you aren't 'splitting' or 'joining' the square root, so it's okay. You aren't turning \(\sqrt{4xy - 4y^2}\) into \(\sqrt{4xy}-\sqrt{4y^2}\), after all (that would be against the rules). You're just squaring the entire expression, which is fine. For instance, this is okay:

\(\sqrt{9 + 16} = \sqrt{x}\)

\(9 + 16 = x\)

We just squared both sides of the equation, which is always allowed.
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Re: substraction/addition inside square roots   [#permalink] 13 Nov 2017, 12:52
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