# How do you simplify sqrt(50a^3b^5)?

Jan 5, 2017

5ab²sqrt(2ab)

#### Explanation:

$\sqrt{50 {a}^{3} {b}^{5}}$

Factorise the terms within the square root.

$\sqrt{5 \times 5 \times 2 \cdot a \times a \times a \cdot b \times b \times b \times b \times b}$

Group the pairs.

$\sqrt{5 \times 5 \cdot a \times a \cdot b \times b \cdot b \times b \cdot 2 \cdot a \cdot b}$

Simplify by removing the pairs.

5ab²sqrt(2ab)

Note that this has been solved with the condition that $a , b \ge 0$.