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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 168 (page 797)

Add and subtract radical expressions in the following exercises, simplify.
(a) $4 \sqrt{5} + 8 \sqrt{5}$
(b) $\sqrt[3]{m} - 4 \sqrt[3]{m}$
(c) $\sqrt{n} + 3 \sqrt{n}$

Short Answer

Expert verified

The values are-

(a) $12 \sqrt{5}$

(b) $- 3 \sqrt[3]{m}$

(c) $4 \sqrt{n}$

Step by step solution

01

Step 1. Solving for (a)

We have $4 \sqrt{5} + 8 \sqrt{5}$ .

Add, because they are like terms.

This will give us,

$= 4 \sqrt{5} + 8 \sqrt{5} = 12 \sqrt{5}$

02

Step 2. Solving for part (b)

We have $\sqrt[3]{m} - 4 \sqrt[3]{m}$ .

Subtract, because they are like terms.

This will give us,

$= \sqrt[3]{m} - 4 \sqrt[3]{m} = - 3 \sqrt[3]{m}$

03

Step 3. Solving for part (c)

We have $\sqrt{n} + 3 \sqrt{n}$ .

Add, because they are like terms.

This will give us,

$= \sqrt{n} + 3 \sqrt{n} = 4 \sqrt{n}$

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Most popular questions from this chapter

Simplify:

$(a) \sqrt{\frac{75}{48}} (b) \sqrt[3]{\frac{54}{250}} (c) \sqrt[4]{\frac{32}{162}}$

In the following exercises, use the Product Property to simplify radical expression $\sqrt{125} .$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{45 p^{9}}}{\sqrt{5 q^{2}}}$

(b) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

(c) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}}$

Simplify:

a. $y^{\frac{3}{4}} 路 y^{\frac{5}{8}}$ b. ${(m^{9})}^{\frac{2}{9}}$ c. $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}}$

Write with a rational exponent:

(a) $\sqrt[5]{a^{2}}$

(b) ${(\sqrt[3]{5 a b})}^{5}$

(c) $\sqrt{{(\frac{7 x y}{z})}^{3}}$

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