Question

If the square root of $8+2\sqrt{15}$ = $\sqrt{5}+\sqrt{k}$. Find k

Answer 1

Consider, $8+2\sqrt{1}5$

$=3+5+2\sqrt{1}5$

$=(\sqrt{3}{)}^2+(\sqrt{5}{)}^2+2\times \sqrt{3}\times \sqrt{5}$

$=(\sqrt{3}+\sqrt{5}{)}^2$

So, Square root of $8+2\sqrt{1}5=(\sqrt{3}+\sqrt{5}{)}^2$

Hence, $k=3$