Chapter 11: Q. 84 (page 1069)

In the following exercises, simplify using absolute value signs as needed.
$a . 8 + \sqrt{96} b . \frac{8 - \sqrt{80}}{4}$

Short Answer

Expert verified

The simplified expressions are,

$a . 8 + 4 \sqrt{6} . b . 2 - \sqrt{5}$

Step by step solution

Given expressions are,

$a . 8 + \sqrt{96} b . \frac{8 - \sqrt{80}}{4}$

The objective is, we need to find the simplified expressions for the given expressions.

The product property for the root is,

$\sqrt[n]{a b} = \sqrt[n]{a} . \sqrt[n]{b}$ and $\sqrt[n]{a} . \sqrt[n]{b} = \sqrt[n]{a b}$

Also we know that, $\sqrt[n]{a^{n}} = a$ .

Part a Step 2: localid="1645429507768" 8 + 96.

$8 + \sqrt{96} = 8 + \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3} = 8 + \sqrt{{(2)}^{4} \times 6}$

Now use the product property rule.

$8 + \sqrt{96} = 8 + \sqrt{{(2)}^{4}} . \sqrt{6} = 8 + 2^{2} . \sqrt{6} = 8 + 4 \sqrt{6}$

Part b Step 3:localid="1645429548860" 8-804

$\frac{8 - \sqrt{80}}{4} = \frac{8 - \sqrt{2 \times 2 \times 2 \times 2 \times 5}}{4} = \frac{8 - \sqrt{{(4)}^{2} \times 5}}{4}$

Now use the product property rule.

$\frac{8 - \sqrt{80}}{4} = \frac{8 - \sqrt{{(4)}^{2}} . \sqrt{5}}{4} = \frac{8 - 4 \sqrt{5}}{4} = 2 - \sqrt{5}$

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In the following exercises, simplify using absolute value signs as needed.
$a . 8 + \sqrt{96} b . \frac{8 - \sqrt{80}}{4}$

Short Answer

Step by step solution

Given expressions are,

Part a Step 2: localid="1645429507768" 8 + 96.

Part b Step 3:localid="1645429548860" 8-804

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In the following exercises, simplify using absolute value signs as needed.a.8+96b.8−804

Short Answer

Step by step solution

Given expressions are,

Part a Step 2: localid="1645429507768" 8 + 96.

Part b Step 3:localid="1645429548860" 8-804

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Geometry

Mechanics Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed.
$a . 8 + \sqrt{96} b . \frac{8 - \sqrt{80}}{4}$