Question

$\sqrt{7 + 2 \sqrt{10} }$
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Answer 1

Answer:

$\sqrt{7 + 2 \sqrt{10} } \\ = \sqrt{5 + 2 + 2 \sqrt{10} } \\ = \sqrt{ {( \sqrt{5} )}^{2} + { (\sqrt{2} )}^{2} + 2 \times \sqrt{5} \times \sqrt{2} } \\ = \sqrt{{( \sqrt{5} )}^{2} + { (\sqrt{2} )}^{2} + 2 \times \sqrt{5 \times 2} } \\ = \sqrt{{( \sqrt{5} )}^{2} + { (\sqrt{2} )}^{2} + 2 \sqrt{10} } \\ = \sqrt{( \sqrt{5} + \sqrt{2} ) ^{2} } \\ = \sqrt{5} + \sqrt{2} \\ thus \\ \sqrt{7 + 2 \sqrt{10} }= \sqrt{5} + \sqrt{2}$