Question

Rationalise the denominators of the following:$\frac{1}{\sqrt{7}}$,$\frac{1}{\sqrt{7}-\sqrt{6}}$,$\frac{1}{\sqrt{5}+\sqrt{2}}$,$\frac{1}{\sqrt{7}-2}$

Answer 1

Part (A)

$\frac{1}{\sqrt{7}}$

$=\frac{1}{\sqrt{7}}\times \frac{\sqrt{7}}{\sqrt{7}}$ Rationalize

$=\frac{\sqrt{7}}{7}$ Ans.

Part (B)

$\frac{1}{\sqrt{7}-\sqrt{6}}$

$=\frac{1}{\sqrt{7}-\sqrt{6}}\times \frac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}$ Rationalize

$=\frac{\sqrt{7}+\sqrt{6}}{{\left(\sqrt{7}\right)}^2-{\left(\sqrt{6}\right)}^2}$

$=\frac{\sqrt{7}+\sqrt{6}}{7-6}$

$=\sqrt{7}+\sqrt{6}$ Ans.

Part (C)

$\frac{1}{\sqrt{5}+\sqrt{2}}$

$=\frac{1}{\sqrt{5}+\sqrt{2}}\times \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}$ Rationalize

$=\frac{\sqrt{5}-\sqrt{2}}{{\left(\sqrt{5}\right)}^2-{\left(\sqrt{2}\right)}^2}$

$=\frac{\sqrt{5}-\sqrt{2}}{5-2}$

$=\frac{\sqrt{5}-\sqrt{2}}{3}$ Ans.

Part (D)

$\frac{1}{\sqrt{7}-2}$

$=\frac{1}{\sqrt{7}-2}\times \frac{\sqrt{7}-2}{\sqrt{7}-2}$

$=\frac{\sqrt{7}-2}{{\left(\sqrt{7}\right)}^2-{\left(2\right)}^2}$

$=\frac{\sqrt{7}-2}{7-4}$

Rationalize

$=\frac{\sqrt{7}-2}{3}$ Ans.