Question

СРОЧНО!!!!
упростите выражение (√6-4√2+√6+4√2)^2

Answer 1

$(\sqrt{6-4\sqrt{2}}+\sqrt{6+4\sqrt{2}})^{2} =(\sqrt{4-4\sqrt{2}+2}+\sqrt{4+4\sqrt{2}+2})^{2} =\\\\=(\sqrt{2^{2} -2*2*\sqrt{2}+(\sqrt{2} )^{2}}+\sqrt{2^{2} +2*2*\sqrt{2}+(\sqrt{2})^{2}})^{2}=\\\\=(\sqrt{(2-\sqrt{2})^{2}}+\sqrt{(2+\sqrt{2})^{2}})^{2}=(2-\sqrt{2}+2+\sqrt{2})^{2}=4^{2}=16\\\\Otvet:\boxed{16}$