Question

find the value of
$\sqrt{5 + 2 \sqrt{6} }$
​

Answer 1

Answer:

➢$\sf{\sqrt{3}+\sqrt{2}}$

Explanation:

$\sf{\sqrt{5+2\sqrt{6}}}$can be written in the form $\sf{(a+b)^2=a^2+b^2+2ab}$ as,

➾$\sf{\sqrt{5+2\sqrt{6}}\:=\: \sqrt{3+2+2\sqrt{3}×\sqrt{2}}}$

➾$\sf{\sqrt{\sqrt{(3)^2}+\sqrt{(2)^2}+2\sqrt{3}×\sqrt{2}}}$

➾$\sf{\sqrt{(\sqrt{3}+\sqrt{2})^2}}$

➾$\sf{\sqrt{3}+\sqrt{2}}$

Answer 2

Answer:

√(3+2+2×√3×√2)

=√3+√2

Hope it helps you...

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