Chapter 7.4, Problem 32PPS

To determine

To simplify the given expression $\sqrt{32r^2{k}^4{t}^5}$ .

Answer to Problem 32PPS

  $4r{k}^2{t}^2\sqrt{2t}$

Explanation of Solution

Given: $\sqrt{32r^2{k}^4{t}^5}$

Calculation:

  $\begin{array}{l}=\sqrt{32r^2{k}^4{t}^5}\\ =\sqrt{2\times 2\times 2\times 2\times 2\times r^2\times {\left(k^2\right)}^2\times t^2\times t^2\times t}\\ =2\times 2\times r\times k^2\times t\times t\times \sqrt{2\times t}\\ =4r{k}^2{t}^2\sqrt{2t}\end{array}$

Thus, obtained form is the simplified form of the given expression.