Question

$sqrt[3]{5 sqrt{2} - 7 } times sqrt{3 + 2 sqrt{2} } =$

Answer 1

$sqrt[3]{5sqrt{2}-7}*sqrt{3+2sqrt{2}}=sqrt[3]{2sqrt{2}-3*2+3sqrt{2}-1}*sqrt{1+2sqrt{2}+2}$

$=sqrt[3]{(sqrt{2})^3-3*(sqrt{2})^2+3sqrt{2}-1^3}*sqrt{1^2+2sqrt{2}+(sqrt{2})^2}=sqrt[3]{(sqrt{2}-1)^3}*sqrt{(1+sqrt{2})^2}=(sqrt{2}-1)*(1+sqrt{2})=2-1=1$

Answer 2

спасибо)