Chapter A.2, Problem 46E

(a)

To determine

To simplify: the expression $\sqrt{\frac{{18}^2}{z^3}}$ .

Answer to Problem 46E

The simplification of $\sqrt{\frac{{18}^2}{z^3}}$ is $\frac{18}{z}\sqrt{\frac{1}{z}}$ .

Explanation of Solution

Given:

The expression is $\sqrt{\frac{{18}^2}{z^3}}$ .

Calculation:

Simplify the expression as follows:

  $\begin{array}{l}\Rightarrow \sqrt{\frac{{18}^2}{z^3}}\\ \Rightarrow \sqrt{\frac{18\times 18}{z\times z\times z}}\\ \Rightarrow \frac{18}{z}\sqrt{\frac{1}{z}}\end{array}$

Thus, the simplification of $\sqrt{\frac{{18}^2}{z^3}}$ is $\frac{18}{z}\sqrt{\frac{1}{z}}$ .

(b)

To determine

To simplify: the expression $\sqrt{\frac{32a^4}{b^2}}$ .

Answer to Problem 46E

The simplification of $\sqrt{\frac{32a^4}{b^2}}$ is $\frac{4a^2}{b}\sqrt{2}$ .

Explanation of Solution

Given:

The expression is $\sqrt{\frac{32a^4}{b^2}}$ .

Calculation:

Simplify the expression as follows:

  $\begin{array}{l}\Rightarrow \sqrt{\frac{32a^4}{b^2}}\\ \Rightarrow \sqrt{\frac{2\times 2\times 2\times 2\times 2\times a^2\times a^2}{b\times b}}\\ \Rightarrow \frac{2\times 2\times a^2}{b}\sqrt{2}\\ \Rightarrow \frac{4a^2}{b}\sqrt{2}\end{array}$

Thus, the simplification of $\sqrt{\frac{32a^4}{b^2}}$ is $\frac{4a^2}{b}\sqrt{2}$ .