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.

_________________