Chapter 7, Problem 8PT

To determine

To Simplify: The expression $\sqrt[5]{3125}$

Answer to Problem 8PT

  $\sqrt[5]{3125}=5$

Explanation of Solution

Given information:

The expression $\sqrt[5]{3125}$

Concept and Formula Used:

Rule of exponent.

  $\sqrt[n]{a}=a^{\frac{1}{n}},{\left(ab\right)}^n=a^n{b}^n$

BODMAS rule

Calculation:

The given expression is

  $\begin{array}{l}\sqrt[5]{3125}\\ \text{Using }\sqrt[n]{a}=a^{\frac{1}{n}}\\ \sqrt[5]{3125}={\left(3125\right)}^{\frac{1}{5}}\\ \sqrt[5]{3125}={\left(5\times 5\times 5\times 5\times 5\right)}^{\frac{1}{5}}\\ \sqrt[5]{3125}={\left(5^5\right)}^{\frac{1}{5}}\\ \text{Using}{\left(a^m\right)}^n=a^{mn}\\ \sqrt[5]{3125}={\left(5\right)}^{5\times \frac{1}{5}}\\ \sqrt[5]{3125}={\left(5\right)}^1\\ \sqrt[5]{3125}=5\end{array}$

Conclusion:

  $\sqrt[5]{3125}=5$