Chapter 6.1, Problem 5WE

(a)

To determine

To simplify: The given expression and identify if the expression represents the real number.

Answer to Problem 5WE

The simplified value of the given expression is $0.1$ . The number $0.1$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{0.01}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{0.01}\\ =\sqrt{\left(\frac{1}{100}\right)}\\ =\sqrt{\frac{1}{10}\times \frac{1}{10}}\\ =\frac{1}{10}\\ =0.1\end{array}$

Any number measurable on the number line whether positive, negative, and decimal or in fractions is called the real number.

Here, the number $0.1$ is the real number.

Therefore, the simplified value of the given expression is $0.1$ . The number $0.1$ is the real number.

(b)

To determine

To simplify: The given expression and identify if the expression represents the real number.

Answer to Problem 5WE

The simplified value of the given expression is $0.1i$ . The number $0.1i$ is not the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{-0.01}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{-0.01}\\ =\sqrt{-\left(\frac{1}{100}\right)}\\ =\sqrt{-\left(\frac{1}{10}\times \frac{1}{10}\right)}\\ =\frac{1}{10}\sqrt{-1}\\ =0.1i\end{array}$

Any number measurable on the number line whether positive, negative, and decimal or in fractions is called the real number.

Here, the number $\sqrt{-1}=i$ is not the real number.

Therefore, the simplified value of the given expression is $0.1i$ . The number $0.1i$ is not the real number.

(c)

To determine

To simplify: The given expression and identify if the expression represents the real number.

Answer to Problem 5WE

The simplified value of the given expression is $-12$ . The number $-12$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt[3]{0.001}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt[3]{0.001}\\ =\sqrt[3]{\frac{1}{1000}}\\ =\sqrt[3]{\frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}}\\ =\frac{1}{10}\\ =0.1\end{array}$

Any number measurable on the number line whether positive, negative, and decimal or in fractions is called the real number.

Here, the number $0.1$ is the real number.

Therefore, the simplified value of the given expression is $0.1$ . The number $0.1$ is the real number.

(d)

To determine

To simplify: The given expression and identify if the expression represents the real number.

Answer to Problem 5WE

The simplified value of the given expression is $-0.1$ . The number $-0.1$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt[3]{-0.001}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt[3]{-0.001}\\ =\sqrt[3]{-\frac{1}{1000}}\\ =\sqrt[3]{-\left(\frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}\right)}\\ =-\frac{1}{10}\\ =-0.1\end{array}$

Any number measurable on the number line whether positive, negative, and decimal or in fractions is called the real number.

Here, the number $-0.1$ is the real number.

Therefore, the simplified value of the given expression is $-0.1$ . The number $-0.1$ is the real number.