Question

If 36 sqrt2 - 24 sqrt2 = sqrtN, what is N?

Answer 1

N = 288

First, both 36 sqrt 2 and 24 sqrt 2 have the common sqrt 2, which means you can directly subtract them.

36 sqrt 2 - 24 sqrt 2 = 12 sqrt 2
12 is outside of the square root means it was a perfect square, thus 12*12 = 144.

There's still a 2 left in the sqrt, and 144 * 2 = 288.

Answer 2

$36\sqrt{2} - 24\sqrt{2}$
$=12 \sqrt{2}$
$= \sqrt{144} * \sqrt{2}$
$\sqrt{144*2}$
$= \sqrt{288}$

In short, N = 288.

Hope this helps !

Photon