Question

What is the simplified form of the following expression?

Answer 1

Option C:

`$\frac{\sqrt[3]{100 x}}{5}=\sqrt[3]{(4 x)/(5)}`

Solution:

Given expression is

`$\sqrt[3]{(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]{(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]{(20x)/(125) }`

Cancel the common factor in both numerator and denominator.

`$=\sqrt[3]{(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]{(100x)/(125) }`

Cancel the common factor in both numerator and denominator.

`$=\sqrt[3]{(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]{(4 x)/(5)}`