Chapter 11: Q. 178 (page 1069)

In the following exercises, simplify.
a. $\sqrt{48 b^{5}} - \sqrt{75 b^{5}}$
b. $8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}}$

Short Answer

Expert verified

On simplification, we get $- b^{2} \sqrt{3 b}, 17 q^{2}$ respectively

Step by step solution

Part (a) Step 1: Given information

Given the expression $\sqrt{48 b^{5}} - \sqrt{75 b^{5}}$

Part (a) Step 2: Simplifying the radical and combine like terms

Simplifying radical and combining we get

$\sqrt{48 b^{5}} - \sqrt{75 b^{5}} = \sqrt{16 b^{4} \cdot 3 b} - \sqrt{25 b^{4} \cdot 3 b} \sqrt{48 b^{5}} - \sqrt{75 b^{5}} = \sqrt{16 b^{4}} \cdot \sqrt{3 b} - \sqrt{25 b^{4}} \cdot \sqrt{3 b} \sqrt{48 b^{5}} - \sqrt{75 b^{5}} = 4 b^{2} \sqrt{3 b} - 5 b^{2} \sqrt{3 b} \sqrt{48 b^{5}} - \sqrt{75 b^{5}} = - b^{2} \sqrt{3 b}$

Part (b) Step 1: Given information

Given expression $8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}}$

Part (b) Step 2: Simplifying the radical and combine like terms

Simplifying radical and combining we get

$8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}} = 8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}} 8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}} = 8 \cdot \sqrt[3]{{(4 q^{2})}^{3}} - 3 \cdot \sqrt[3]{{(5 q^{2})}^{3}} 8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}} = 8 \cdot 4 q^{2} - 3 \cdot 5 q^{2} 8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}} = 32 q^{2} - 15 q^{2} 8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}} = 17 q^{2}$

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In the following exercises, simplify.
a. $\sqrt{48 b^{5}} - \sqrt{75 b^{5}}$
b. $8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}}$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Simplifying the radical and combine like terms

Part (b) Step 1: Given information

Part (b) Step 2: Simplifying the radical and combine like terms

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In the following exercises, simplify.a.48b5-75b5b.864q63-3125q63

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Simplifying the radical and combine like terms

Part (b) Step 1: Given information

Part (b) Step 2: Simplifying the radical and combine like terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
a. $\sqrt{48 b^{5}} - \sqrt{75 b^{5}}$
b. $8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}}$