Question

Find the square root of the following in the form of a binomial surd.
$8+2\sqrt{7}$.

Answer 1

Let $x=\sqrt{8+2\sqrt{7}}=\sqrt{n}+\sqrt{m}$

$8+2\sqrt{7}=n+m+2\sqrt{nm}$

Hence, $n+m=8,nm=7$

$n^2-8n+7=0$

$n=7$ or $n=1$

Similarily, $m=1$ or $m=7$