Question

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

Answer 1

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

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