1. ## Adding Square Roots raised to a power

When studying for the GMAT, I encountered this problem

(Square root of 3+Square root of 3+Square root of 3)^2

As in raised to the second power.

I know the answer is 27. However, I was under the impression that squaring a square root would simply remove the square root symbol. Why wouldn't this answer be 3+3+3=9?

2. ## Re: Adding Square Roots raised to a power

$\displaystyle \dipslaystyle (\sqrt{3}+\sqrt{3}+\sqrt{3})^2 = (3\sqrt{3})^2 = \dots$

Originally Posted by KingNathan

I know the answer is 27. However, I was under the impression that squaring a square root would simply remove the square root symbol. Why wouldn't this answer be 3+3+3=9?

$\displaystyle \dipslaystyle (a+b)^2 = a^2+2ab+b^2 \neq a^2+b^2$

3. ## Re: Adding Square Roots raised to a power

Originally Posted by pickslides
$\displaystyle \dipslaystyle (\sqrt{3}+\sqrt{3}+\sqrt{3})^2 = (3\sqrt{3})^2 = \dots$

$\displaystyle \dipslaystyle (a+b)^2 = a^2+2ab+b^2 \neq a^2+b^2$
That makes complete sense! Thank you very much.