Question

Simplified form of the expression $2\sqrt{x^3}\times x\sqrt[3]{3a}$ can be:

• A. $2x^2\sqrt[5]{5a^2{x}^3}$
• B. $2x^2\sqrt[3]{3a^2{x}^3}$
• C. $2x^2\sqrt[6]{6a^3{x}^3}$
• D. $2x^2\sqrt[6]{6a^2{x}^3}$

Answer 1

Answer: (D)

$2x^2\sqrt[6]{6a^2{x}^3}$

The simplified form of $2\sqrt{x^3}\times x\sqrt[3]{3a}$ is

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

$=2x\times x^{\frac{9}{6}}\times a^{\frac{2}{6}}$

$=2x\times \sqrt[6]{6x^9\times a^2}$

$=2x^2\times \sqrt[6]{6x^3.a^2}$

$=2x^2\sqrt[6]{6a^2{x}^3}$