Chapter 46, Problem 1A

Solve $\sqrt[3]{x}=\frac{1}{5}.$Express the answer as both a common fraction and a decimal fraction.

To determine

To solve $\sqrt[3]{x}=\frac{1}{5}$ and express the answer as a common fraction and a decimal fraction.

Answer to Problem 1A

The expression $\sqrt[3]{x}=\frac{1}{5}$ is solved and expressed as common fraction as $\frac{1}{125}$ and as decimal fraction as $\frac{8}{1000}$.

Explanation of Solution

Given information:

Given expression, $\sqrt[3]{x}=\frac{1}{5}$

Calculation:

We know that a common fraction is a fraction in which numerator and denominator are both integers, as opposed to fractions.

And a decimal fraction is a fraction whose denominator is 10 or a multiple of 10 like 100, 1000,10000.

Given expression, $\sqrt[3]{x}=\frac{1}{5}$

Taking cube of both sides,

  $\begin{array}{l}x={\left(\frac{1}{5}\right)}^3\\ =\frac{1}{125}\end{array}$

Common fraction: $\frac{1}{125}$

Decimal fraction: $\frac{1}{125}=0.0008=\frac{8}{1000}$

Hence, the expression $\sqrt[3]{x}=\frac{1}{5}$ is solved and expressed as common fraction as $\frac{1}{125}$ and as decimal fraction as $\frac{8}{1000}$.