Chapter R.7, Problem 1E

Simplify each expression by removing as many factors as possible from under the radical. Assume that all variables represent positive real numbers.

$\sqrt[3]{125}$

To determine

The simplified expression for the radical $\sqrt[3]{125}$.

Answer to Problem 1E

Solution: $\sqrt[3]{125}=\underset{\_}{5}$

Explanation of Solution

Given: The radical $\sqrt[3]{125}$.

Explanation:

Simplify the radical as follows:

$\begin{array}{c}\sqrt[3]{125}=\sqrt[3]{{\left(5\right)}^3}\\ ={\left(5\right)}^{3\times \frac{1}{3}}\\ =5\end{array}$

Conclusion: The simplified expression for the radical is $\underset{\_}{5}$.