Chapter 11.6, Problem 4ST

To determine

To approximate: the given square root to the nearest tenth.

Answer to Problem 4ST

  $\sqrt{144m^2{n}^2}=12mn$ .

Explanation of Solution

Given:

The given square root is $\sqrt{144m^2{n}^2}$ .

Calculation:

As the given square root is $\sqrt{144m^2{n}^2}$ .

Therefore, the given square root to the nearest tenth is

  $\begin{array}{l}\sqrt{144m^2{n}^2}=\sqrt{144}\times \sqrt{m^2{n}^2}\\ =\sqrt{{12}^2}\times \sqrt{{\left(mn\right)}^2}\left\{\text{simplify}\right\}\\ =12mn\{\because \sqrt{a^2}=a\}\end{array}$

Hence, the value of the given square root to the nearest tenth is $\sqrt{144m^2{n}^2}=12mn$ .