# How do you simplify sqrt162?

Oct 14, 2015

We simplify this by removing the perfect squares...

#### Explanation:

The trick to this problem is to realize that $\sqrt{x y}$ can be simplified if either $x$ or $y$ is a perfect square. So, if we have $\sqrt{16 y}$, and we know that the square root of 16 is 4, we can rewrite this as $4 \sqrt{y}$. Do you see? We need to do some factoring to get rid of all of the perfect squares under the sqrt sign, until we're left with a number that isn't a perfect square.

So, for the problem $\sqrt{162}$, can we remove any perfect squares? If we think for a moment, we can see that $162 = 81 \cdot 2$, and 81 is a perfect square ($9 x 9 = 81$). So this can be rewritten as

$\sqrt{\left(81\right) \cdot \left(2\right)}$

We can take the square root of 81 to get:

$9 \sqrt{2}$

which is as simplified as we can get in this case.