Chapter 6.2, Problem 31WE

To determine

Simplify the expression $\sqrt{32}$ .

Answer to Problem 31WE

The simplified value is $4\sqrt{2}$ .

Explanation of Solution

Given information: The given expression is,

  $\sqrt{32}\mathrm{......}\left(1\right)$

Calculation: Simplify (1),

  $\begin{array}{c}\sqrt{32}=\sqrt{\left(16\right)\left(2\right)}\\ =\left(\sqrt{16}\right)\left(\sqrt{2}\right)\mathrm{......}\left(\sqrt{ab}=\left(\sqrt{a}\right)\left(\sqrt{b}\right)\right)\\ =4\sqrt{2}\end{array}$

To determine

Simplify the expression $\sqrt[3]{32}$ .

Answer to Problem 31WE

The simplified value is $2\sqrt[3]{4}$ .

Explanation of Solution

Given information: The given expression is,

  $\sqrt[3]{32}\mathrm{......}\left(2\right)$

Calculation: Simplify (2),

  $\begin{array}{c}\sqrt[3]{32}=\sqrt[3]{\left(8\right)\left(4\right)}\\ =\left(\sqrt[3]{8}\right)\left(\sqrt[3]{4}\right)\mathrm{......}\left\{\sqrt[3]{ab}=\left(\sqrt[3]{a}\right)\left(\sqrt[3]{b}\right)\right\}\\ =2\sqrt[3]{4}\end{array}$

To determine

Simplify the expression $\sqrt[4]{32}$ .

Answer to Problem 31WE

The simplified value is $2\sqrt[4]{2}$ .

Explanation of Solution

Given information: The given expression is,

  $\sqrt[4]{32}\mathrm{......}\left(3\right)$

Calculation: Simplify (3),

  $\begin{array}{c}\sqrt[4]{32}=\sqrt[4]{\left(16\right)\left(2\right)}\\ =\left(\sqrt[4]{16}\right)\left(\sqrt[4]{2}\right)\mathrm{......}\left\{\sqrt[n]{ab}=\left(\sqrt[n]{a}\right)\left(\sqrt[n]{b}\right)\right\}\\ =2\sqrt[4]{2}\end{array}$

To determine

Simplify the expression $\sqrt[5]{32}$ .

Answer to Problem 31WE

The simplified value is $2$ .

Explanation of Solution

Given information: The given expression is,

  $\sqrt[5]{32}\mathrm{......}\left(4\right)$

Calculation: Simplify (4),

  $\begin{array}{c}\sqrt[5]{32}=\sqrt[5]{{\left(2\right)}^5}\\ =2\end{array}$