Chapter 6.1, Problem 6WE

(a)

To determine

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

Answer to Problem 6WE

The simplified value of the given expression is $0.2$ . The number $0.2$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{0.04}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{0.04}\\ =\sqrt{\frac{4}{100}}\\ =\sqrt{\frac{2\times 2}{10\times 10}}\\ =\frac{2}{10}\\ =0.2\end{array}$

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

Here, the number $0.2$ is the real number.

Therefore, the simplified value of the given expression is $0.2$ . The number $0.2$ is the real number.

(b)

To determine

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

Answer to Problem 6WE

The simplified value of the given expression is $-0.2$ . The number $-0.2$ is the real number.

Explanation of Solution

Given:

The given expression is

  $-\sqrt{0.04}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{0.04}\\ =\sqrt{\frac{4}{100}}\\ =\sqrt{\frac{2\times 2}{10\times 10}}\\ =\frac{2}{10}\\ =0.2\end{array}$

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

Here, the number $-0.2$ is the real number.

Therefore, the simplified value of the given expression is $-0.2$ . The number $-0.2$ is the real number.

(c)

To determine

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

Answer to Problem 6WE

The simplified value of the given expression is $0.02$ . The number $0.02$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{0.0004}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{0.0004}\\ =\sqrt{\frac{4}{10000}}\\ =\sqrt{\frac{2\times 2}{100\times 100}}\\ =\frac{2}{100}\\ =0.02\end{array}$

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

Here, the number $0.02$ is the real number.

Therefore, the simplified value of the given expression is $0.02$ . The number $0.02$ is the real number.

(d)

To determine

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

Answer to Problem 6WE

The simplified value of the given expression is $0.02i$ . The number $0.02i$ is not the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{-0.0004}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{-0.0004}\\ =\sqrt{-\left(\frac{4}{10000}\right)}\\ =\sqrt{-\left(\frac{2}{100}\times \frac{2}{100}\right)}\\ =\frac{2}{100}\sqrt{-1}\\ =0.02i\end{array}$

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 $0.02i$ . The number $0.02i$ is not the real number.