Question

Rationalize the denominator and simplify:

(i) $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

(ii) $\frac{5+2\sqrt{3}}{7+4\sqrt{3}}$

Answer 1

(i)$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

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

$=\frac{3+2-2\sqrt{6}}{3-2}$

$=5-2\sqrt{6}$

(ii)

$\frac{5+2\sqrt{3}}{7+4\sqrt{3}}$

=$\frac{5+2\sqrt{3}}{7+4\sqrt{3}}\times \frac{7-4\sqrt{3}}{7-4\sqrt{3}}$

$=\frac{\sqrt{11}-6\sqrt{3}}{49-48}$

$=11-6\sqrt{3}$