Question

Simplify (square root of 2)(cube root of 2)

Answer 1

$\sqrt{2} \sqrt[3]{2} =$

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

$= 2^{\frac{1}{2} + \frac{1}{3}}$

$= 2^{\frac{3}{6} + \frac{2}{6}}$

$= 2^{\frac{5}{6}}$

$= \sqrt[6]{2^5}$