How do you simplify 25/sqrt15?

Jun 3, 2016

$\frac{5}{3} \sqrt{15}$

Explanation:

To simplify this fraction we have to $\textcolor{b l u e}{\text{rationalise the denominator}}$ That is make it a rational value.

We make use of the following fact : $\sqrt{a} \times \sqrt{a} = a$

hence : $\sqrt{15} \times \sqrt{15} = 15 \text{ a rational value}$

Since this is a fraction, however, we must multiply both the numerator and denominator by the same value.

$\Rightarrow \frac{25}{\sqrt{15}} = \frac{25}{\sqrt{15}} \times \frac{\sqrt{15}}{\sqrt{15}} = \frac{25 \sqrt{15}}{15} = \frac{5}{3} \sqrt{15}$