Chapter 7.5, Problem 3STP

For Exercises $1-4,$ choose the correct letter.

Which of the following expressions is equivalent to $(\sqrt{144a^3})-(\sqrt[3]{27b^2})$?

A. $9{(ab)}^{\frac{3}{2}}$

B. $12a^{\frac{3}{2}}-3b^{\frac{2}{3}}$

C. $12a^3-3b^2$

D. ${(144a)}^{\frac{3}{2}}-{(27b)}^{\frac{2}{3}}$

To determine

To find: The correct expression for $\left(\left(\sqrt{144a^3}\right)-\left(\sqrt[3]{27b^2}\right)\right)$

Answer to Problem 3STP

The correct expression is $12a^{\frac{3}{2}}-3b^{\frac{2}{3}}$ .

Explanation of Solution

Given:

The provided expression is:

  $\left(\left(\sqrt{144a^3}\right)-\left(\sqrt[3]{27b^2}\right)\right)$

Calculation:

The provided expression could be simplified as:

  $\begin{array}{c}\left(\left(\sqrt{144a^3}\right)-\left(\sqrt[3]{27b^2}\right)\right)={\left(144a^3\right)}^{\frac{1}{2}}-{\left(27b^2\right)}^{\frac{1}{3}}\\ =12a^{\frac{3}{2}}-3b^{\frac{2}{3}}\end{array}$

Thus, the correct expression is

  $12a^{\frac{3}{2}}-3b^{\frac{2}{3}}$ .

Hence, the correct option is (B).