Question

Rationalize the denominator.

(i) $\frac{3}{\sqrt{5}}$ (ii) $\frac{1}{\sqrt{14}}$ (iii) $\frac{5}{\sqrt{7}}$ (iv) $\frac{6}{9\sqrt{3}}$ (v) $\frac{11}{\sqrt{3}}$

Answer 1

(i) $\frac{3}{\sqrt{5}}$

$$\begin{gathered} =\frac{3}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}} \\ =\frac{3\sqrt{5}}{{\left(\sqrt{5}\right)}^2} \\ =\frac{4\sqrt{5}}{5} \end{gathered}$$

(ii) $\frac{1}{\sqrt{14}}$

$$\begin{gathered} =\frac{1}{\sqrt{14}}\times \frac{\sqrt{14}}{\sqrt{14}} \\ =\frac{\sqrt{14}}{{\left(\sqrt{14}\right)}^2} \\ =\frac{\sqrt{14}}{14} \end{gathered}$$

(iii) $\frac{5}{\sqrt{7}}$

$$\begin{gathered} =\frac{5}{\sqrt{7}}\times \frac{\sqrt{7}}{\sqrt{7}} \\ =\frac{5\sqrt{7}}{{\left(\sqrt{7}\right)}^2} \\ =\frac{5\sqrt{7}}{7} \end{gathered}$$

(iv) $\frac{6}{9\sqrt{3}}$

$$\begin{gathered} =\frac{2}{3\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}} \\ =\frac{2\sqrt{3}}{3\times 3} \\ =\frac{2\sqrt{3}}{9} \end{gathered}$$

(v) $\frac{11}{\sqrt{3}}$

$$\begin{gathered} =\frac{11}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}} \\ =\frac{11\sqrt{3}}{{\left(\sqrt{3}\right)}^2} \\ =\frac{11\sqrt{3}}{3} \end{gathered}$$