sqrt{5+2 sqrt{6}} = dots | vedclass

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Question

(D) To simplify the expression $\sqrt{5+2 \sqrt{6}}$,we look for two numbers whose sum is $5$ and whose product is $6$.These two numbers are $3$ and $

Vedclass · Accepted Answer

$\sqrt{3}+\sqrt{2}$

Vedclass · Answer

(D) To simplify the expression $\sqrt{5+2 \sqrt{6}}$,we look for two numbers whose sum is $5$ and whose product is $6$.These two numbers are $3$ and $2$.We can rewrite the expression as:$\sqrt{5+2 \sqrt{6}} = \sqrt{(3+2)+2 \sqrt{3 	imes 2}}$Using the algebraic identity $(a+b)^2 = a^2+b^2+2ab$,we have:$\sqrt{3+2+2 \sqrt{3} \sqrt{2}} = \sqrt{(\sqrt{3})^2+(\sqrt{2})^2+2 \sqrt{3} \sqrt{2}}$$= \sqrt{(\sqrt{3}+\sqrt{2})^2}$$= \sqrt{3}+\sqrt{2}$

$\sqrt{5+2 \sqrt{6}} = \dots$

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