Chapter 8: Q 8.72 (page 790)

Simplify
$5 \sqrt{3} - 9 \sqrt{3}$
$5 \sqrt[3]{y} + 3 \sqrt[3]{y}$
$5 \sqrt[4]{m} - 2 \sqrt[3]{m}$

Short Answer

Expert verified

Part a. $- 4 \sqrt{3}$

Part b. $8 \sqrt[3]{y}$

Part c. $5 \sqrt[4]{m} - 2 \sqrt[3]{m}$

Step by step solution

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

In the expression $5 \sqrt{3} - 9 \sqrt{3}$ , the radicals are like. So we subtract the coefficients to get the simplified expression.

$\begin{array}{rcl} 5 \sqrt{3} - 9 \sqrt{3} & = & (5 - 9) \sqrt{3} \\ = & - 4 \sqrt{3} \end{array}$

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

In the expression $5 \sqrt[3]{y} + 3 \sqrt[3]{y}$ , the radicals are like. So we add the coefficients to get the simplified expression.

$\begin{array}{rcl} 5 \sqrt[3]{y} + 3 \sqrt[3]{y} & = & (5 + 3) \sqrt[3]{y} \\ = & 8 \sqrt[3]{y} \end{array}$

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

In the given expression $5 \sqrt[4]{m} - 2 \sqrt[3]{m}$ the radicals are the same but the indices are different. So they are not like radicals.

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

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Simplify
$5 \sqrt{3} - 9 \sqrt{3}$
$5 \sqrt[3]{y} + 3 \sqrt[3]{y}$
$5 \sqrt[4]{m} - 2 \sqrt[3]{m}$

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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Simplify53-935y3+3y35m4-2m3

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

Applied Mathematics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Simplify
$5 \sqrt{3} - 9 \sqrt{3}$
$5 \sqrt[3]{y} + 3 \sqrt[3]{y}$
$5 \sqrt[4]{m} - 2 \sqrt[3]{m}$