Question

Rationalise the denominator of $\frac{1}{4+\sqrt{5}}$

Answer 1

$\frac{1}{4+\sqrt{5}}$

Multiply nominator and denominator by $4-\sqrt{5}$ we get

$\frac{1\times (4-\sqrt{5})}{(4+\sqrt{5})(4-\sqrt{5})}$

$=\frac{4-\sqrt{5}}{(4{)}^2-(\sqrt{5}{)}^2}$

$=\frac{4-\sqrt{5}}{16-5}$

$=\frac{4-\sqrt{5}}{11}$