# How do you simplify sqrt(20y^5)?

Sep 18, 2015

$\sqrt{20 {y}^{5}} = 2 {y}^{2} \sqrt{5 y}$

#### Explanation:

We know we can only take perfect squares out of the root, so we have to find the square factors in 20 and in ${y}^{5}$

The latter is easy, we know that ${y}^{5} = {y}^{2} \cdot {y}^{2} \cdot y$, so we can take out two $y$s

$\sqrt{20 {y}^{5}} = {y}^{2} \sqrt{20 y}$

20 is more complicated, but not hard. We just need to factor it, i.e.: see every prime integer divisor it has in order.

20 | 2
10 | 2
5 | 5
1 | / $5 \cdot {2}^{2}$

So we know we can take a 2 out.

$\sqrt{20 {y}^{5}} = 2 {y}^{2} \sqrt{5 y}$