Chapter 6.1, Problem 11WE

(a)

To determine

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

Answer to Problem 11WE

The simplified value of the given expression is $10$ . The number $10$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{{10}^2}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{{10}^2}\\ =\sqrt{10\times 10}\\ =10\end{array}$

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

Here, the number $10$ is the real number.

Therefore, the simplified value of the given expression is $10$ . The number $10$ is the real number.

(b)

To determine

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

Answer to Problem 11WE

The simplified value of the given expression is $100$ . The number $100$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{{10}^4}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{{10}^4}\\ =\sqrt{10\times 10\times 10\times 10}\\ =100\end{array}$

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

Here, the number $100$ is the real number.

Therefore, the simplified value of the given expression is $100$ . The number $100$ is the real number.

(c)

To determine

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

Answer to Problem 11WE

The simplified value of the given expression is $1000$ . The number $1000$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{{10}^6}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{{10}^6}\\ =\sqrt{10\times 10\times 10\times 10\times 10\times 10}\\ =10\times 10\times 10\\ =1000\end{array}$

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

Here, the number $1000$ is the real number.

Therefore, the simplified value of the given expression is $1000$ . The number $1000$ is the real number.

(d)

To determine

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

Answer to Problem 11WE

The simplified value of the given expression is ${10}^{10}$ . The number ${10}^{10}$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{{10}^6}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{{10}^{20}}\\ ={10}^{\frac{1}{2}\times 20}\\ ={10}^{10}\end{array}$

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

Here, the number ${10}^{10}$ is the real number.

Therefore, the simplified value of the given expression is ${10}^{10}$ . The number ${10}^{10}$ is the real number.