Question

If $\sqrt{13+m\sqrt{10}}=\sqrt{8}+\sqrt{5}$ than find value of $m$.

Answer 1

$\sqrt{13+m\sqrt{10}}=\sqrt{8}+\sqrt{5}$

squaring both sides

$13+m\sqrt{10}=(\sqrt{8}+\sqrt{5}{)}^2=8+5+2\sqrt{8\times 5}$

$13+m\sqrt{10}=13+2\times 2\sqrt{10}$

$m\sqrt{10}=4\sqrt{10}$

$\Rightarrow m=4$