Question

Simplify $\frac{1}{2-\sqrt{7}}$ by rationalising the denominator.

• A. $-\frac{2+\sqrt{7}}{3}$
• B. $-\frac{2-\sqrt{3}}{3}$
• C. $\frac{2-\sqrt{3}}{3}$
• D. $\frac{2+\sqrt{7}}{3}$

Answer 1

The correct option is A

$-\frac{2+\sqrt{7}}{3}$

The least rationalising factor of $\frac{1}{2-\sqrt{7}}$ is $2+\sqrt{7}$

So, multiplying and dividing by $2+\sqrt{7}$, we get,

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

$=\frac{2+\sqrt{7}}{2^2-{\sqrt{7}}^2}$

$=-\frac{2+\sqrt{7}}{3}$