Question

Rationalise the denominator and simplify:

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

Answer 1

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

Multiplying both numerator and denominator by $7-4\sqrt{3}$ to rationalise the denominator.

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

$=\frac{35-20\sqrt{3}+14\sqrt{3}-24}{7^2-(4\sqrt{3}{)}^2}$

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

$=\frac{11-6\sqrt{3}}{1}$

$=11-6\sqrt{3}$