Question

Rationalise the denominator of $\frac{1}{\sqrt{3}-\sqrt{2}}$.

• A. $\sqrt{3}+\sqrt{2}$
• B. $\sqrt{5}+\sqrt{2}$
• C. $\sqrt{3}-\sqrt{2}$
• D. $\sqrt{5}+\sqrt{3}$

Answer 1

The correct option is A

$\sqrt{3}+\sqrt{2}$

Rationalising factor of $\frac{1}{\sqrt{3}-\sqrt{2}}$ is $\sqrt{3}+\sqrt{2}$ .

Multiplying both the numerator and denominator with $\sqrt{3}+\sqrt{2}$, we get

$\frac{1}{\sqrt{3}-\sqrt{2}}$ $\times$ $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

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

= $\sqrt{3}+\sqrt{2}$