Question

Find the square root of the following in the form of a binomial surd.
$12+2\sqrt{35}$.

Answer 1

Let $x=\sqrt{12+2\sqrt{35}}=\sqrt{n}+\sqrt{m}$

$12+2\sqrt{35}=n+m+2\sqrt{nm}$

Hence, $n+m=12,nm=35$

$n^2-12n+35=0$

$n=7$ or $n=5$

Similarily, $m=5$ or $m=7$