Question

What is the simplified form of the following expression?

Answer 1

Option C:

$\frac{\sqrt[3]{100 x}}{5}=\sqrt[3]{\frac{4 x}{5}}$

Solution:

Given expression is

$\sqrt[3]{\frac{4 x}{5}}$

Note: $\sqrt[3]{125}=\sqrt[3]{{5^3}} = 5$

To find the correct expression for the above simplified expression.

Option A: $\frac{\sqrt[3]{4 x}}{5}$

5 can be written as $\sqrt[3]{125}$.

$\frac{\sqrt[3]{4 x}}{5}=\frac{\sqrt[3]{4 x}}{\sqrt[3]{125} }$

       $=\sqrt[3]{\frac{4x}{125} }$

It is not the given simplified expression.

Option B: $\frac{\sqrt[3]{20 x}}{5}$

$\frac{\sqrt[3]{20 x}}{5}=\frac{\sqrt[3]{20 x}}{\sqrt[3]{125} }$

         $=\sqrt[3]{\frac{20x}{125} }$

Cancel the common factor in both numerator and denominator.

         $=\sqrt[3]{\frac{4x}{25} }$

It is not the given simplified expression.

Option C: $\frac{\sqrt[3]{100 x}}{5}$

$\frac{\sqrt[3]{100 x}}{5}=\frac{\sqrt[3]{100 x}}{\sqrt[3]{125} }$

           $=\sqrt[3]{\frac{100x}{125} }$

Cancel the common factor in both numerator and denominator.

           $=\sqrt[3]{\frac{4 x}{5}}$

It is the given simplified expression.

Option D: $\frac{\sqrt[3]{100 x}}{125}$

$\frac{\sqrt[3]{100 x}}{125}=\frac{\sqrt[3]{100 x}}{5^3}$

It is not the given simplified expression.

Hence Option C is the correct answer.

$\frac{\sqrt[3]{100 x}}{5}=\sqrt[3]{\frac{4 x}{5}}$