Question

Find the product of $\sqrt{2}$ and $\sqrt[3]{35}$.

Answer 1

Solution:

Product of $\sqrt{2}$ and $\sqrt[3]{35}=\sqrt{2}\times \sqrt[3]{35}$

$=2^{\frac{1}{2}}\times 5^{\frac{1}{3}}$

$=(2^3{)}^{\frac{1}{6}}\times (5^2{)}^{\frac{1}{6}}$

$=8^{\frac{1}{6}}\times {25}^{\frac{1}{6}}$

$=(8\times 25{)}^{\frac{1}{6}}$

$={200}^{\frac{1}{6}}$