Question

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

• A. cube root of the square root of x
• B. sixth root of the fifth power of x
• C. fifth root of the sixth power of x
• D. sixth root of x

Answer 1

Answer: (B)

Since the square root of $x=\sqrt{x}$ and the cube root of $x=\sqrt[3]{3x}$
and their product $=\sqrt{x}\times \sqrt[3]{3x}$
= $x^{\frac{1}{2}}$ $\times$$x^{\frac{1}{3}}$ [Since, $\sqrt[n]{na}=a^{\frac{1}{n}}$]
$=x^{\frac{1}{2}+\frac{1}{3}}$ [Since, $a^m\times a^n=a^{m+n}$]
$=x^{\frac{3+2}{6}}$
$=x^{\frac{5}{6}}$
Therefore, required product is $=\sqrt[6]{6x^5}$