Question

Найдите значение выражения
$( \sqrt{6 - 4 \sqrt{2} } + \sqrt{6 + 4 \sqrt{2) {}^{2} } }$
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Answer 1

Привет!)

$(\sqrt{6-4\sqrt{2} }+\sqrt{6+4\sqrt{2} } )^{2}=(\sqrt{(2-\sqrt{2})^{2}}+ \sqrt{(2+\sqrt{2})^{2}})^{2}=(2-\sqrt{2}+2+\sqrt{2} )^{2}=4^{2} =16$

Answer 2

$6-4\sqrt{2}+6+4\sqrt{2}+2\sqrt{(6-4\sqrt{2})(6+4\sqrt{2})}=12+2\sqrt{36-32}=12+4=16$