Question

Rationalizing the denominator of the following.
(i) $\frac{3}{\sqrt{5}}$
(ii) $\frac{2}{3\sqrt{3}}$
(iii) $\frac{1}{\sqrt{12}}$
(vi) $\frac{2\sqrt{7}}{\sqrt{11}}$
(v) $\frac{3\sqrt[3]{35}}{\sqrt[3]{39}}$.

Answer 1

$\left(i\right)\frac{3}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{3}}=\frac{3\sqrt{5}}{5}$

$\left(ii\right)\frac{2}{3\sqrt{3}}\times \frac{3\sqrt{3}}{3\sqrt{3}}=\frac{6\sqrt{3}}{27}=\frac{2\sqrt{3}}{9}$

$\left(iii\right)\frac{1}{\sqrt{12}}\times \frac{\sqrt{12}}{\sqrt{12}}=\frac{\sqrt{12}}{12}$

$\left(iv\right)\frac{2\sqrt{7}}{\sqrt{11}}\times \frac{\sqrt{11}}{\sqrt{11}}=\frac{2\sqrt{77}}{11}$

$\left(v\right)\frac{33\sqrt{5}}{3\sqrt{9}}\times \frac{3\sqrt{9}}{3\sqrt{9}}\times \frac{3\sqrt{9}}{3\sqrt{9}}$

$=\frac{33\sqrt{81\times 5}}{9}=\frac{93\sqrt{15}}{9}$

$=3\sqrt{15}$