Chapter 13.9, Problem 50HP

To determine

To identify the correct answer.

Answer to Problem 50HP

D. $6\sqrt{4g^2}$

Explanation of Solution

Given: g is a positive number and an expression equal to 12g is to be identified from the given options.

Calculation: Simplify each option.

  $\begin{array}{l}\sqrt{144g}\\ =\sqrt{144}\times \sqrt{g}\\ =12\sqrt{g}\\ \\ \sqrt{12g^2}\\ =\sqrt{12}\times \sqrt{g^2}\\ =\sqrt{12}g\\ \\ \sqrt{24g^2}\\ =\sqrt{24}\times \sqrt{g^2}\\ =2\sqrt{6}\times g\\ =2\sqrt{6}g\\ \\ 6\sqrt{4g^2}\\ =6\times \sqrt{4}\times \sqrt{g^2}\\ =6\times 2\times g\\ =12g\end{array}$

Thus, we can see that option D is the required answer.