# How do you simplify 3/sqrt(7)?

Aug 9, 2016

$\frac{3 \sqrt{7}}{7}$

#### Explanation:

Simplifying this fraction means expressing it without the radical on the denominator. This is called $\textcolor{b l u e}{\text{rationalising the denominator}}$

To do this we make use of the following fact.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\sqrt{a} \times \sqrt{a} = {\left(\sqrt{a}\right)}^{2} = a} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \sqrt{7} \times \sqrt{7} = 7$

Since this is a fraction, if we multiply the denominator by some value then we must multiply the numerator by the same value.

multiply both numerator and denominator by $\sqrt{7}$

$\Rightarrow \frac{3}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{3 \times \sqrt{7}}{\sqrt{7} \times \sqrt{7}} = \frac{3 \sqrt{7}}{7}$