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Q. The product of \( \sqrt{x} \) and \( \sqrt[3]{x} \), is
(a) \( \sqrt[3]{\sqrt{x}} \)
(b) \( \sqrt[6]{x^5} \)
(c) \( \sqrt[5]{x^6} \)
(d) \( \sqrt[6]{x} \)
✏️ Solution
\( \sqrt{x} \times \sqrt[3]{x} \)
\( = x^{1/2} \times x^{1/3} \)
\( = x^{\left(\frac{1}{2}+\frac{1}{3}\right)} \)
\( = x^{\frac{5}{6}} \)
\( = \sqrt[6]{x^5} \)
Correct Option: (b) \( \sqrt[6]{x^5} \)
\( \boxed{\sqrt[6]{x^5}} \)