# How do you simplify -sqrt338-sqrt200+sqrt162?

Apr 13, 2018

$- 14 \sqrt{2}$

#### Explanation:

You could try using the Fundamental Theorem of Arithmetic to express all those integers as the product of their primes.

$338 = {2}^{1} \times {13}^{2}$
$200 = {2}^{3} \times {5}^{2}$
$162 = {2}^{1} \times {3}^{4}$

What this tells us is that they all have a common factor of 2
$\gcd \left(338 , 200 , 162\right) = 2$

Since the expression contains the square root of each that means the entire expression has a factor of $\sqrt{2}$, so we can rewrite it as

$\sqrt{2} \left(- \sqrt{{13}^{2}} - \sqrt{{2}^{2} {5}^{2}} + \sqrt{{3}^{4}}\right)$
As we can see these all contain even powers and can thus be simplified!

$\sqrt{2} \left(- 13 - 10 + 9\right)$

$\sqrt{2} \left(- 14\right)$

$- 14 \sqrt{2}$