Question: Roots and Squares

Comment on Roots and Squares

Why do you not FOIL quantity A since it is squared?
greenlight-admin's picture

FOIL only applies to the product of binomials in the form (a+b) or (a-b). For more on this, see: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Is it correct to say that (√x)^2 always equals √(x^2) ?
greenlight-admin's picture

The identity (√x)^2 = √(x^2) is true only for values of x such that x ≥ 0.

For negative values, however, the equation doesn't hold true. For example, let's see what happens if x = -9

We get: (√-9)^2 = √(-9^2)
Since we cannot find the square root of -9, our calculations end there.

ASIDE: In math classes where students learn about complex (aka imaginary) numbers, it is taught that (√-9) = 3i, where i is an imaginary number such that i² =-1. However, the GRE is concerned with REAL NUMBERS only. So, we cannot allow imaginary numbers (like i) into our calculations.

root(16)= +- 4. why do you take only +4? Isn't the correct answer D?
greenlight-admin's picture

The square root NOTATION tells us to take only the positive root.

So, √9 = 3 and √49 = 7.

Cheers,
Brent

So, is it like, when there is square root symbol, we only take the positive root?

And when we are told to find the roots of x^2, we take both the positive and negative roots?

I'm always confused when to take negative root and when not while finding square root.
greenlight-admin's picture

That's perfect summary of how roots and squares work!

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