Chapter 6.1, Problem 10WE

(a)

To determine

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

Answer to Problem 10WE

The simplified value of the given expression is $\frac{1}{4}$ . The number $\frac{1}{4}$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{\frac{1}{16}}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{\frac{1}{16}}\\ =\sqrt{\frac{1}{4\times 4}}\\ =\frac{1}{4}\end{array}$

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

Here, the number $\frac{1}{4}$ is the real number.

Therefore, the simplified value of the given expression is $\frac{1}{4}$ . The number $\frac{1}{4}$ is the real number.

(b)

To determine

The simplified value of the given expression is $\frac{9}{4}$ . The number $\frac{9}{4}$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt{\frac{81}{16}}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt{\frac{81}{16}}\\ =\sqrt{\frac{9\times 9}{4\times 4}}\\ =\frac{9}{4}\end{array}$

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

Here, the number $\frac{1}{8}$ is the real number.

Therefore, the simplified value of the given expression is $\frac{9}{4}$ . The number $\frac{9}{4}$ is the real number.

(c)

To determine

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

Answer to Problem 10WE

The simplified value of the given expression is $\frac{1}{2}$ . The number $\frac{1}{2}$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt[4]{\left(\frac{1}{16}\right)}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt[4]{\left(\frac{1}{16}\right)}\\ =\sqrt[4]{\left(\frac{1}{2\times 2\times 2\times 2}\right)}\\ ={\left(\frac{1}{2}\right)}^{4\times \frac{1}{4}}\\ =\frac{1}{2}\end{array}$

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

Here, the number $\frac{1}{2}$ is the real number.

Therefore, the simplified value of the given expression is $\frac{1}{2}$ . The number $\frac{1}{2}$ is the real number.

(d)

To determine

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

Answer to Problem 10WE

The simplified value of the given expression is $\frac{3}{2}$ . The number $\frac{3}{2}$ is the real number.

Explanation of Solution

Given:

The given expression is

  $\sqrt[4]{\left(\frac{81}{16}\right)}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=\sqrt[4]{\left(\frac{81}{16}\right)}\\ =\sqrt[4]{\left(\frac{3\times 3\times 3\times 3}{2\times 2\times 2\times 2}\right)}\\ ={\left(\frac{3}{2}\right)}^{4\times \frac{1}{4}}\\ =\frac{3}{2}\end{array}$

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

Here, the number $\frac{3}{2}$ is the real number.

Therefore, the simplified value of the given expression is $\frac{3}{2}$ . The number $\frac{3}{2}$ is the real number.