Question

Rationalize the denominator of the following
$\left(i\right)\frac{2}{3\sqrt{3}}\left(ii\right)\frac{\sqrt{40}}{\sqrt{3}}$

[ 3 marks ]

Answer 1

$\text{(i) Let}E=\frac{2}{3\sqrt{3}}$
For rationalising the denominator, multiply
numerator and denominator by $\sqrt{3}$,
$E=\frac{2}{3\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3\times 3}=\frac{2\sqrt{3}}{9}$

[ 1.5 marks ]

$\text{(ii)Let}E=\frac{\sqrt{40}}{\sqrt{3}}$
For rationailsing the denominator, multiply numerator and denominator by $\sqrt{3}$,
$E=\frac{\sqrt{40}}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{40\times 3}}{(\sqrt{3}{)}^2}=\frac{\sqrt{120}}{3}=\frac{\sqrt{2\times 2\times 2\times 5\times 3}}{3}=\frac{2}{3}\sqrt{30}$

[ 1.5 marks ]