# How do you simplify 2/(3sqrt63) ?

Mar 18, 2018

Shown below...

#### Explanation:

We need to rationalise the denominator, in this case multiply both numerator and denominator by $\sqrt{63}$

$\implies \frac{2}{3 \sqrt{63}} \cdot \frac{\sqrt{63}}{\sqrt{63}}$

$\implies \frac{2 \sqrt{63}}{3 \cdot 63}$

$\implies \frac{2 \cdot \sqrt{3 \cdot 3 \cdot 7}}{189}$

$\implies \frac{6 \sqrt{7}}{189}$

$\implies \frac{2 \sqrt{7}}{63}$

Mar 18, 2018

$\frac{2 \sqrt{7}}{63}$

#### Explanation:

$\frac{2}{3 \sqrt{63}}$

$\therefore = \frac{2}{3 \sqrt{3 \cdot 3 \cdot 7}}$

$\therefore \sqrt{3} \cdot \sqrt{3} = 3$

$\therefore = \frac{2}{3 \cdot 3 \sqrt{7}}$

$\therefore = \frac{2}{9 \sqrt{7}}$

$\therefore = \frac{2}{9 \sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}}$

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

$\therefore = \frac{2 \sqrt{7}}{9 \times 7}$

$\therefore = \frac{2 \sqrt{7}}{63}$