Question

Rationalise the denominator
2/7+4✓3

Answer 1

     

$\frac{2}{7+4\sqrt{3}} \ = \ \frac{2(7-4\sqrt{3})}{(7+4\sqrt{3})(7-4\sqrt{3})} \ = \ \frac{14-8\sqrt{3}}{7^2-(4\sqrt{3})^2}\ = \ \frac{14-8\sqrt{3}}{49-48}\ = \ \frac{14-8\sqrt{3}}{1} \\ \\ = \bold{14-8\sqrt{3}}$

 

$\therefore\ \frac{2}{7+4\sqrt{3}}\ = \ \bold{14-8\sqrt{3}}$