Question

Simplify the expression and choose the correct option

$\sqrt[2]{28}$$\times$$\sqrt[3]{312}$$\times$$\sqrt[6]{69}$

• A. $4\times \sqrt[6]{6162}$
• B. $2\times \sqrt[6]{681}$
• C. $4\times \sqrt[6]{681}$
• D. $8\times \sqrt[6]{6162}$

Answer 1

The correct option is A

$4\times \sqrt[6]{6162}$

The given expression $\sqrt[2]{28}$$\times$$\sqrt[3]{312}$$\times$$\sqrt[6]{69}$ can be written as

$\Rightarrow (8{)}^{\frac{1}{2}}\times (12{)}^{\frac{1}{3}}\times (9{)}^{\frac{1}{6}}=((2{)}^3{)}^{\frac{1}{2}}\times (\left(2{)}^2\right(3){)}^{\frac{1}{3}}\times ((3{)}^2{)}^{\frac{1}{6}}=(2{)}^{\frac{3}{2}}\times \left(2{)}^{\frac{2}{3}}\right(3{)}^{\frac{1}{3}}\times (3{)}^{\frac{1}{3}}=(2{)}^{\frac{13}{6}}\times (3{)}^{\frac{2}{3}}=(2{)}^{\frac{13}{6}}\times (3{)}^{\frac{4}{6}}=(2{)}^2(2{)}^{\frac{1}{6}}\times (3{)}^{\frac{4}{6}}=4\left(\right(2\left)\right(3{)}^4{)}^{\frac{1}{6}}=4\left(\right(2\left)\right(81){)}^{\frac{1}{6}}=4(162{)}^{\frac{1}{6}}$