# How do you simplify sqrt(15/36)?

May 3, 2017

$\sqrt{\frac{15}{36}} = \frac{\sqrt{15}}{6}$

#### Explanation:

Here are a couple of identities we will use:

If $a \ge 0$ and $b > 0$ then:

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

If $a \ge 0$ then:

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

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Example

When given $\sqrt{\frac{15}{36}}$ to simplify, you could simplify $\frac{15}{36}$ first, split the square root, then rationalise the denominator, but that would be missing out on the fact that $36 = {6}^{2}$ is already a perfect square.

Instead, we can proceed as follows:

$\sqrt{\frac{15}{36}} = \sqrt{\frac{15}{6} ^ 2} = \frac{\sqrt{15}}{\sqrt{{6}^{2}}} = \frac{\sqrt{15}}{6}$