Question

Вычислить значение выражения:

Answer 1

$sqrt{11+6sqrt{2}}+sqrt{11-6sqrt{2}}=sqrt{(sqrt{11+6sqrt{2}}+sqrt{11-6sqrt{2}})^2}=$

$sqrt{(sqrt{11+6sqrt{2}})^2+2sqrt{11+6sqrt{2}}*sqrt{11-6sqrt{2}}+(sqrt{11-6sqrt{2}})^2}}=$

$sqrt{11+6sqrt{2}+2sqrt{11^2-6^2*2}+11-6sqrt{2}}=sqrt{22+2*7}=6$