Question

The value of $3\sqrt[3]{35}\times 7\sqrt[3]{310}\times 5\sqrt[3]{320}$ is

• A. 1050
• B. 1500
• C. 950
• D. 1005

Answer 1

The correct option is A

1050

$3\sqrt[3]{35}\times 7\sqrt[3]{310}\times 5\sqrt[3]{320}$
$\Rightarrow 3\times (5{)}^{\frac{1}{3}}\times 7\times (10{)}^{\frac{1}{3}}\times 5\times (20{)}^{\frac{1}{3}}$
$\because (ab{)}^m=(a^m)\times (b^m)$
$\Rightarrow (3\times 7\times 5)\times (5\times 10\times 20{)}^{\frac{1}{3}}$
$\Rightarrow 105\times (5\times 10\times 2\times 10{)}^{\frac{1}{3}}$

$\Rightarrow \left[105\right]\times [{10}^3{]}^{\frac{1}{3}}$

$\because (a^m{)}^n=(a{)}^{m\times n}$
$\Rightarrow \left[105\right]\times [10{]}^{3\times \frac{1}{3}}=105\times 10=1050$