Question

НАЙДИТЕ ЗНАЧЕНИЕ ВЫРАЖЕНИЯ

$\sqrt[3]{1 + \sqrt{2} } \times \sqrt[6]{3 - 2 \sqrt{2} }$
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Answer 1

$\sqrt[3]{1+\sqrt{2} }\cdot\sqrt[6]{3-2\sqrt{2} }= \sqrt[6]{(1+\sqrt{2})^{2}}\cdot\sqrt[6]{3-2\sqrt{2} }= \sqrt[6]{1+2\sqrt{2}+2 }\cdot\sqrt[6]{3-2\sqrt{2} }=\\\\=\sqrt[6]{(3+2\sqrt{2})(3-2\sqrt{2})}=\sqrt[6]{3^{2}-(2\sqrt{2})^{2}} =\sqrt[6]{9-8}=\sqrt[6]{1} =\boxed1$