The number obtained on rationalising the denominator of ${\dfrac{1}{\sqrt{7} - 2}}$ is

1. ${\dfrac{\sqrt{7} + 2}{3}}$

2. ${\dfrac{\sqrt{7} - 2}{3}}$

3. ${\dfrac{\sqrt{7} + 2}{5}}$

4. ${\dfrac{\sqrt{7} + 2}{45}}$

Given,

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

Let us rationalise the denominator,

Then,

${\dfrac{1}{\sqrt{7} - 2}} = {\dfrac{1}{\sqrt{7} - 2}} × \dfrac{\sqrt{7} + 2}{\sqrt{7} + 2} \\[1.5em] \Rightarrow \dfrac{\sqrt{7} + 2}{(\sqrt{7})^2 - {2}^2} \\[1.5em] \Rightarrow \dfrac{\sqrt{7} + 2}{7 - 4} \\[1.5em] \Rightarrow \dfrac{\sqrt{7} + 2}{3} \\[1.5em]$

∴ Option 1, is the correct option.