Question

решить уравнение ³√8х=√2*³√2

Answer 1

$\sqrt[3]{8x} = \sqrt{2} \sqrt[3]{2} \\ \sqrt[3]{8x} = \sqrt[6]{ {2}^{3} } \sqrt[6]{ {2}^{2} } \\ \sqrt[3]{8x} = \sqrt[6]{ {2}^{3} {2}^{2} } \\ \sqrt[3]{8x} = \sqrt[6]{ {2}^{5} } \\ ( \sqrt[3]{8x} ) {}^{3} = ( \sqrt[6]{32} ) {}^{3} \\ 8x = \sqrt{32} \\ x = \frac{ \sqrt{32} }{8} \\ x = \frac{4 \sqrt{2} }{8} \\ x = \frac{ \sqrt{2} }{2}$