# How do you simplify sqrt(108x^3y^5 )?

Jan 28, 2017

$6 x {y}^{2} \sqrt{3 y}$

#### Explanation:

We are looking for values that are squared. These can be taken outside the square root in non-squared form.

Using a factor tree to deal with the number 108

So the prime factors are: ${2}^{2} \times {3}^{2} \times 3$

${x}^{3}$ is the same as: ${x}^{2} \times x$
${y}^{5}$ is the same as: ${y}^{2} \times {y}^{2} \times y$

Thus write: $\sqrt{108 {x}^{3} {y}^{5}}$ as $\sqrt{{2}^{2} \times {3}^{3} \times 3 \times {x}^{2} \times x \times {y}^{2} \times {y}^{2} \times y}$

Taking the squared values outside the root gives:

$2 \times 3 \times x \times {y}^{2} \times \sqrt{3 x y}$

$6 x {y}^{2} \sqrt{3 x y}$