Question

State True or False, if the expression $\frac{1}{\sqrt{3}+\sqrt{2}}$$=\sqrt{3}-\sqrt{2}$, after rationalising the denominator.

• A. True
• B. False

Answer 1

The correct option is A True

As given $\frac{1}{\sqrt{3}+\sqrt{2}}$

Multiply and divide by $\sqrt{3}-\sqrt{2}$

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

$=\frac{\sqrt{3}-\sqrt{2}}{{\left(\sqrt{3}\right)}^2-{\left(\sqrt{2}\right)}^2}$

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

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

Hence the answer is True.