Question

$\sqrt{10} x = \frac{\sqrt{5^{2}*20} }{\sqrt[3]{10} }$

Answer 1

$\sqrt{10}x=\frac{\sqrt{5^2\cdot 20}}{\sqrt[3]{10}}\\\\\sqrt{10}x=\frac{5\cdot \sqrt{4\cdot 5}}{\sqrt[3]{10}}\\\\\sqrt{10}x=\frac{5\cdot 2\sqrt5}{\sqrt[3]{10}}\\\\x=\frac{10\sqrt5}{\sqrt[3]{10}\cdot \sqrt{10}}\\\\x=\frac{10\sqrt5}{\sqrt[6]{10^2}\cdot \sqrt[6]{10^3}}=\frac{10\sqrt5}{\sqrt[6]{10^2\cdot 10^3}}=\frac{10\sqrt5}{\sqrt[6]{10^6}}=\frac{10\sqrt5}{10}=\sqrt5\\\\x=\sqrt5$