Question

The value of $3\sqrt[3]{32}\times 7\sqrt[3]{36}\times 5\sqrt[3]{318}$ is:

• A. 545
• B. 500
• C. 630
• D. 400

Answer 1

The correct option is C 630

$3\sqrt[3]{32}\times 7\sqrt[3]{36}\times 5\sqrt[3]{318}$
$\Rightarrow 3\times (2{)}^{\frac{1}{3}}\times 7\times (6{)}^{\frac{1}{3}}\times 5\times (18{)}^{\frac{1}{3}}$
Grouping with same powers:
$\Rightarrow 105\times (2\times 6\times 18{)}^{\frac{1}{3}}$
$\Rightarrow 105\times (2\times 6\times 6\times 3{)}^{\frac{1}{3}}$
$\Rightarrow \left[105\right]\times [6{]}^{3\times \frac{1}{3}}=105\times 6=630$