Question

Вычислите:
$1) sqrt{31-6 sqrt{26} } - sqrt{31+6 sqrt{26} } 2) sqrt[3]{5 sqrt{2}-7 } * sqrt{3+2 sqrt{2} }$

Answer 1

$1. sqrt{31-6sqrt{13}}-sqrt{31+6sqrt{13}}=sqrt{ (sqrt{18}- sqrt{13})^2 }-sqrt{ (sqrt{18}+ sqrt{13})^2 }=\ sqrt{18}- sqrt{13}-sqrt{18}- sqrt{13}=-2 sqrt{13} ;\ 2. sqrt[3]{5 sqrt{2}-7 } * sqrt{3+2 sqrt{2} } = sqrt[3]{( sqrt{2}-1 )^3}* sqrt{( sqrt{2}+1 )^2}=\ (sqrt{2}-1)(sqrt{2}+1)=1;$