Question

The product of the square root of $x$ with the cube root of $x$, is

Answer 1

We know that,

Square root of $x=\sqrt{x}=x^{\frac{1}{2}}$

Cube root of $x=\sqrt[3]{3x}=x^{\frac{1}{3}}$

Thus,$x^{\frac{1}{2}}\times x^{\frac{1}{3}}$

$=x^{(\frac{1}{2}+\frac{1}{3})}$

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

$=(x^5{)}^{\frac{1}{6}}$

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

which is sixth root of the fifth power of $x$

Hence, (b) is correct answer.