# What is the square root of a^2\b^5?

May 30, 2018

$= \frac{a \sqrt{b}}{{b}^{3}}$

#### Explanation:

I assume you meant:

$= \sqrt{{a}^{2} / {b}^{5}}$

$= \frac{\sqrt{{a}^{2}}}{\sqrt{{b}^{5}}}$

$= \frac{a}{{b}^{2} \sqrt{b}}$

now you need to rationalize the denominator by multiplying the expression by:

$\frac{\sqrt{b}}{\sqrt{b}}$

$= \frac{a}{{b}^{2} \sqrt{b}} \cdot \frac{\sqrt{b}}{\sqrt{b}}$

$= \frac{a \sqrt{b}}{{b}^{2} \cdot b}$

$= \frac{a \sqrt{b}}{{b}^{3}}$

May 30, 2018

$\frac{a \sqrt{b}}{b} ^ 3$

#### Explanation:

$\sqrt{{a}^{2} / {b}^{5}}$

$\therefore = \frac{\sqrt{{a}^{2}}}{\sqrt{{b}^{5}}}$

$\therefore = \frac{\sqrt{a \cdot a}}{\sqrt{b \cdot b \cdot b \cdot b \cdot b}}$

$\therefore \sqrt{a} \cdot \sqrt{a} = a$

$\therefore \sqrt{b} \cdot \sqrt{b} = b$

$\therefore = \frac{a}{{b}^{2} \sqrt{b}} \times \frac{{b}^{2} \sqrt{b}}{{b}^{2} \sqrt{b}}$

$\therefore = \frac{a {b}^{2} \sqrt{b}}{b} ^ 5$

$\therefore = \frac{a \sqrt{b}}{b} ^ \left(5 - 2\right)$

$\therefore = \frac{a \sqrt{b}}{b} ^ 3$