Chapter 11.6, Problem 3MRE

To determine

To simplify: the given expression.

Answer to Problem 3MRE

  $\sqrt{50a^5{\left(b+4\right)}^2}=5a^2\left(b+4\right)\sqrt{2a}$ .

Explanation of Solution

Given:

The given expression is $\sqrt{50a^5{\left(b+4\right)}^2}$ .

Calculation:

As the given expression is $\sqrt{50a^5{\left(b+4\right)}^2}$ .

Therefore, the given expression is expressed as,

  $\begin{array}{l}\sqrt{50a^5{\left(b+4\right)}^2}=\sqrt{50}\times \sqrt{a^5}\times \sqrt{{\left(b+4\right)}^2}\\ \left\{\begin{array}{l}\sqrt{50}=\sqrt{25\times 2}=5\sqrt{2}\\ \sqrt{a^5}=\sqrt{{\left(a^2\right)}^2\times a}=a^2\sqrt{a}\\ \sqrt{{\left(b+4\right)}^2}=\left(b+4\right)\{\because \sqrt{a^2}=a\}\end{array}\right\}\\ \sqrt{50a^5{\left(b+4\right)}^2}=5\sqrt{2}\times a^2\sqrt{a}\times \left(b+4\right)\\ =5a^2\left(b+4\right)\sqrt{2a}\end{array}$

Thus, $\sqrt{50a^5{\left(b+4\right)}^2}=5a^2\left(b+4\right)\sqrt{2a}$

Hence, the simplified form of the given expression is $\sqrt{50a^5{\left(b+4\right)}^2}=5a^2\left(b+4\right)\sqrt{2a}$ .