Question

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

Answer 1

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