Question

Write the reciprocal of $5+\sqrt{2}$.

Answer 1

Reciprocal of $5+\sqrt{2}=\frac{1}{5+\sqrt{2}}$

(Rationalising its denominator)

$=\frac{1(5-\sqrt{2})}{(5+\sqrt{2})(5-\sqrt{2})}$

$=\frac{5-\sqrt{2}}{(5{)}^2-(\sqrt{2}{)}^2}=\frac{5-\sqrt{2}}{25-2}=\frac{5-\sqrt{2}}{23}$