State whether the statement is True/False.

The simplified form of $2 \sqrt{x^{3}} \times x \sqrt[3]{a}$ is $2 x^{2} \sqrt[6]{a^{2} x^{3}}$

True

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False

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Solution

The correct option is A True

$L . H . S = 2 \sqrt{x^{3}} \times x \sqrt[3]{a} = 2. x^{\frac{1}{3}} . x . a^{\frac{1}{3}} = 2. x . x^{\frac{1}{2}} \times x . a^{\frac{1}{3}}$

$= 2 x^{2} . x^{1 / 2} . a^{1 / 3} = 2 x^{2} . (a^{2} . x^{3})^{1 / 6} = 2 x^{2} . \sqrt[6]{a^{2} . x^{3}} = R . H . S$

$∵ L . H . S = R . H . S$

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

Hence, it is True

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