Question

Find the product of $\sqrt[3]{33}\times \sqrt{3}\times \sqrt[3]{32}$

• A. $\sqrt[6]{6972}$
• B. $\sqrt[6]{6672}$
• C. $\sqrt[3]{3972}$
• D. $\sqrt[12]{12972}$

Answer 1

Answer: (A)

$\sqrt[6]{6972}$

$\sqrt[3]{33}\times \sqrt{3}\times \sqrt[3]{32}$

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

$=9^{\frac{1}{6}}\times {27}^{\frac{1}{6}}\times 4^{\frac{1}{6}}$

$=\sqrt[6]{6972}$