Chapter 7, Problem 7PT

To determine

To Simplify: The expression $\sqrt[3]{1000}$

Answer to Problem 7PT

  $\sqrt[3]{1000}=10$

Explanation of Solution

Given information:

The expression $\sqrt[3]{1000}$

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

  $\begin{array}{l}\sqrt[3]{1000}\\ \text{Using }\sqrt[n]{a}=a^{\frac{1}{n}}\\ \sqrt[3]{1000}={\left(1000\right)}^{\frac{1}{3}}\\ \sqrt[3]{1000}={\left(10\times 10\times 10\right)}^{\frac{1}{3}}\\ \sqrt[3]{1000}={\left({10}^3\right)}^{\frac{1}{3}}\\ \text{Using}{\left(a^m\right)}^n=a^{mn}\\ \sqrt[3]{1000}={\left(10\right)}^{3\times \frac{1}{3}}\\ \sqrt[3]{1000}={\left(10\right)}^1\\ \sqrt[3]{1000}=10\end{array}$

Conclusion:

  $\sqrt[3]{1000}=10$