Question

EVALUATE:
$\sqrt{5 + 2 \sqrt{6} }$
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Answer 1

Answer:

Required value of√[ 5 + 2√6 ] is √2 + √3.

Step-by-step explanation:

$\implies\sqrt{5+2\sqrt6}\\\\\implies\sqrt{2+3+2\sqrt{3\times2}}\\\\\implies\sqrt{(\sqrt2)^2 + (\sqrt3)^2 + 2( \sqrt3 \times \sqrt2 ) }$

From the properties of factorisation :

• a^2 + b^2 + 2ab

Therefore, { continued }

$\sqrt{(\sqrt2 + \sqrt3)^2}\\\\\implies\sqrt2+\sqrt3$

Hence the required value of√[ 5 + 2√6 ] is √2 + √3.