Question

Rationalise the denominator and simplify
$\frac{5\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

Answer 1

$\frac{5\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

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

$=\frac{(5\sqrt{3}+\sqrt{2})(\sqrt{3}+\sqrt{2})}{3-2}$ $[\because a^2-b^2=(a-b\left)\right(a+b\left)\right]$

$=(5\times 3\times 3+5\times 3\times 2+2\times 3+2\times 2)$

$=45+30+6+4$

$=85$