Q 8.71. Simplify:聽82-92role="math" loca... [FREE SOLUTION]

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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 8.71. (page 789)

Simplify:
$8 \sqrt{2} - 9 \sqrt{2}$
role="math" localid="1644771286761" $4 \sqrt[3]{x} + 7 \sqrt[3]{x}$
role="math" localid="1644770840204" $3 \sqrt[4]{x} - 5 \sqrt[4]{y}$

Short Answer

Expert verified

Part a. $- \sqrt{2}$

Part b. $11 \sqrt[3]{x}$

Part c.role="math" localid="1644771393584" $3 \sqrt[4]{x} - 5 \sqrt[4]{y}$

Step by step solution

Part (a) Step 1. Subtract the like radicals to simplify

In the expression $8 \sqrt{2} - 9 \sqrt{2}$ , the radicals are like. So we subtract the coefficients to get the simplified expression.

role="math" localid="1644771244647" $\begin{array}{rcl} 8 \sqrt{2} - 9 \sqrt{2} & = & (8 - 9) \sqrt{2} \\ = & - \sqrt{2} \end{array}$

Part (b) Step 1. Add the like radicals to simplify

In the expression $4 \sqrt[3]{x} + 7 \sqrt[3]{x}$ , the radicals are like. So we add the coefficients to get the simplified expression.

$\begin{array}{rcl} 4 \sqrt[3]{x} + 7 \sqrt[3]{x} & = & (4 + 7) \sqrt[3]{x} \\ = & 11 \sqrt[3]{x} \end{array}$

Part (c) Step 1. Check the indices and the radicals

In the given expression $3 \sqrt[4]{x} - 5 \sqrt[4]{y}$ the indices are the same but the radicals are different. So they are not like radicals.

Since the radicals are not like so we cannot subtract them.

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91影视

Simplify:
$8 \sqrt{2} - 9 \sqrt{2}$
role="math" localid="1644771286761" $4 \sqrt[3]{x} + 7 \sqrt[3]{x}$
role="math" localid="1644770840204" $3 \sqrt[4]{x} - 5 \sqrt[4]{y}$

Short Answer

Step by step solution

Part (a) Step 1. Subtract the like radicals to simplify

Part (b) Step 1. Add the like radicals to simplify

Part (c) Step 1. Check the indices and the radicals

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91影视

Simplify:82-92role="math" localid="1644771286761" 4x3+7x3role="math" localid="1644770840204" 3x4-5y4

Short Answer

Step by step solution

Part (a) Step 1. Subtract the like radicals to simplify

Part (b) Step 1. Add the like radicals to simplify

Part (c) Step 1. Check the indices and the radicals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Decision Maths

Logic and Functions

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Simplify:
$8 \sqrt{2} - 9 \sqrt{2}$
role="math" localid="1644771286761" $4 \sqrt[3]{x} + 7 \sqrt[3]{x}$
role="math" localid="1644770840204" $3 \sqrt[4]{x} - 5 \sqrt[4]{y}$