Question

$\sqrt{7 + 2 \sqrt{10} }$

Answer 1

$\sqrt{7+2\sqrt{10}}$

$\implies \sqrt{5+2\sqrt{10}+2}$

$\implies \sqrt{(\sqrt{5})^2+(\sqrt{2})^2+2.\sqrt{5}.\sqrt{2}}$

We know that : $a^2+b^2+2ab=(a+b)^2$

$\implies \sqrt{(\sqrt{5}+\sqrt{2})^2}$

$\implies \sqrt{5}+\sqrt{2}$

The value is : $\boxed{\sqrt{5}+\sqrt{2}}$

Hope it helps ;-)

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