Question

Find the square root of the following in the form of a binomial surd.
$14+6\sqrt{5}$.

Answer 1

Let $x=\sqrt{14+6\sqrt{5}}=\sqrt{n}+\sqrt{m}$

$14+6\sqrt{5}=n+m+2\sqrt{nm}$

Hence, $n+m=14,nm=45$

$n^2-14n+45=0$

$n=9$ or $n=5$

Similarily, $m=5$ or $m=9$