# How do you simplify sqrt(18/5)?

Apr 7, 2018

#### Answer:

See a solution process below:

#### Explanation:

First, we can rewrite and simplify the numerator as:

$\frac{\sqrt{18}}{\sqrt{5}} \implies \frac{\sqrt{9 \cdot 2}}{\sqrt{5}} \implies \frac{\sqrt{9} \sqrt{2}}{\sqrt{5}} \implies \frac{3 \sqrt{2}}{\sqrt{5}}$

Now, if necessary, we can rationalize the denominator by multiplying the fraction by the appropriate form of $1$:

$\frac{\sqrt{5}}{\sqrt{5}} \times \frac{3 \sqrt{2}}{\sqrt{5}} \implies$

$\frac{\sqrt{5} \times 3 \sqrt{2}}{\sqrt{5} \times \sqrt{5}} \implies$

$\frac{3 \sqrt{5} \sqrt{2}}{5} \implies$

$\frac{3 \sqrt{5 \times 2}}{5} \implies$

$\frac{3 \sqrt{10}}{5}$

Or

$\frac{3}{5} \sqrt{10}$