Chapter 8: Q 8.75 (page 791)

Simplify:
$\sqrt{18} + 6 \sqrt{2}$
role="math" localid="1644811385005" $6 \sqrt[3]{16} - 2 \sqrt[3]{250}$
role="math" localid="1644811516386" $\frac{2}{3} \sqrt[3]{81} - \frac{1}{2} \sqrt[3]{24}$

Short Answer

Expert verified

Part a. $9 \sqrt{2}$

Part b. $2 \sqrt[3]{2}$

Part c. $\sqrt[3]{3}$

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} \sqrt{18} + 6 \sqrt{2} & = & \sqrt{9 \cdot 2} + 6 \sqrt{2} \\ = & \sqrt{9} \cdot \sqrt{2} + 6 \sqrt{2} \\ = & 3 \sqrt{2} + 6 \sqrt{2} \end{array}$

On combing the like radicals we get

$\begin{array}{rcl} 3 \sqrt{2} + 6 \sqrt{2} & = & (3 + 6) \sqrt{2} \\ = & 9 \sqrt{2} \end{array}$

Part (b) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} 6 \sqrt[3]{16} - 2 \sqrt[3]{250} & = & 6 \sqrt[3]{8 \cdot 2} - 2 \sqrt[3]{125 \cdot 2} \\ = & 6 \sqrt[3]{8} \cdot \sqrt[3]{2} - 2 \sqrt[3]{125} \cdot \sqrt[3]{2} \\ = & 6 \cdot 2 \cdot \sqrt[3]{2} - 2 \cdot 5 \cdot \sqrt[3]{2} \\ = & 12 \sqrt[3]{2} - 10 \sqrt[3]{2} \end{array}$

On combing the like radicals we get

$\begin{array}{rcl} 12 \sqrt[3]{2} - 10 \sqrt[3]{2} & = & (12 - 10) \sqrt[3]{2} \\ = & 2 \sqrt[3]{2} \end{array}$

Part (c) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} \frac{2}{3} \sqrt[3]{81} - \frac{1}{2} \sqrt[3]{24} & = & \frac{2}{3} \sqrt[3]{27 \cdot 3} - \frac{1}{2} \sqrt[3]{8 \cdot 3} \\ = & \frac{2}{3} \sqrt[3]{27} \cdot \sqrt[3]{3} - \frac{1}{2} \sqrt[3]{8} \cdot \sqrt[3]{3} \\ = & \frac{2}{3} \cdot 3 \cdot \sqrt[3]{3} - \frac{1}{2} \cdot 2 \cdot \sqrt[3]{3} \\ = & 2 \sqrt[3]{3} - \sqrt[3]{3} \end{array}$

On combing the like radicals we get

$\begin{array}{rcl} 2 \sqrt[3]{3} - \sqrt[3]{3} & = & (2 - 1) \sqrt[3]{3} \\ = & \sqrt[3]{3} \end{array}$

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Simplify:
$\sqrt{18} + 6 \sqrt{2}$
role="math" localid="1644811385005" $6 \sqrt[3]{16} - 2 \sqrt[3]{250}$
role="math" localid="1644811516386" $\frac{2}{3} \sqrt[3]{81} - \frac{1}{2} \sqrt[3]{24}$

Short Answer

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Part (b) Step 1. Simplify the radicals and combine like radicals

Part (c) Step 1. Simplify the radicals and combine like radicals

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Simplify:18+62role="math" localid="1644811385005" 6163-22503role="math" localid="1644811516386" 23813-12243

Short Answer

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Part (b) Step 1. Simplify the radicals and combine like radicals

Part (c) Step 1. Simplify the radicals and combine like radicals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Geometry

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify:
$\sqrt{18} + 6 \sqrt{2}$
role="math" localid="1644811385005" $6 \sqrt[3]{16} - 2 \sqrt[3]{250}$
role="math" localid="1644811516386" $\frac{2}{3} \sqrt[3]{81} - \frac{1}{2} \sqrt[3]{24}$