Question

The product cube root of 2 x square root of 4 x 12th root of 32 is equal to: ?

Answer 1

cubed root of 2: $\sqrt[3]{2}$ = $2^{\frac{1}{3}}$

square root of 4: $\sqrt{4}$ = 2¹

12th root of 32: $\sqrt[12]{32}$ = $\sqrt[12]{2^{5}}$ = $2^{\frac{5}{12}}$

$2^{\frac{1}{3}}$ x 2¹ x $2^{\frac{5}{12}}$ = $2^{\frac{1}{3} + 1 + \frac{5}{12} }$ = $2^{\frac{4}{12} + \frac{12}{12} + \frac{5}{12} }$ = $2^{\frac{21}{12}}$ = $2^{\frac{7}{4}}$ = 2$\sqrt[4]{2^{3}}$ = 2$\sqrt[4]{8}$

Answer: 2$\sqrt[4]{8}$