Question

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

Answer 1

$\sqrt[3]{5\sqrt{2}-7}\cdot \sqrt{3+2\sqrt{2}}=\sqrt[3]{(\sqrt{2}-1)^3}\cdot \sqrt{(\sqrt{2}+1)^2}=(\sqrt{2}-1)(\sqrt{2}+1)=\\ \\ \\ =(\sqrt{2})^2-1^2=2-1=1$