Question

вычислите
$\sqrt{6 - \sqrt{11} } + \sqrt{6 + \sqrt{11} }$
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Answer 1

$\sqrt{6-\sqrt{11} }+\sqrt{6+\sqrt{11} }=\sqrt{5,5-\sqrt{11} +0,5}=\\\\=\sqrt{(\sqrt{5,5})^{2}-2*\sqrt{5,5}*\sqrt{0,5}+(\sqrt{0,5})^{2} }} +\sqrt{(\sqrt{5,5})^{2}+2*\sqrt{5,5}*\sqrt{0,5}+(\sqrt{0,5})^{2} }} =\\\\=\sqrt{(\sqrt{5,5}-\sqrt{0,5} )^{2}} +\sqrt{(\sqrt{5,5}+\sqrt{0,5} )^{2}} =|\sqrt{5,5}-\sqrt{0,5}|+|\sqrt{5,5}+\sqrt{0,5} |=\\\\=\sqrt{5,5}-\sqrt{0,5}+\sqrt{5,5}+\sqrt{0,5} =2\sqrt{5,5}$