Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.24 (page 754)

Simplify: $(a) \sqrt{225 m^{2} n^{2}} (b) \sqrt{169 x^{10} y^{14}} (c) \sqrt[3]{27 w^{36} z^{15}}$

Short Answer

Expert verified

The solutions of (a), (b) and (c) are $15 |m n|, 13 |x^{5} y^{7}| a n d 3 w^{12} z^{5}$ respectively.

Step by step solution

Part (a) Step 1. Given information

The root: $\sqrt{225 m^{2} n^{2}}$

Part (a) Step 2. Calculation

We have,

$\sqrt{225 m^{2} n^{2}} = \sqrt{{(15 m n)}^{2}} \sin c e {(15 m n)}^{2} = 225 m^{2} n^{2} = 15 |m n|$

Therefore, the solution is $15 |m n|$

Part (b) Step 1. Given information

The root: $\sqrt{169 x^{10} y^{14}}$

Part (b) Step 2. Calculation

We have,

$\sqrt{169 x^{10} y^{14}} = \sqrt{{(13 x^{5} y^{7})}^{2}} \sin c e {(13 x^{5} y^{7})}^{2} = 169 x^{10} y^{14} = 13 |x^{5} y^{7}|$

Therefore, the solution is $13 |x^{5} y^{7}|$

Part (c) Step 1. Given information

The root: $\sqrt[3]{27 w^{36} z^{15}}$

Part (c) Step 2. Calculation

We have,

$\sqrt[3]{27 w^{36} z^{15}} = \sqrt[3]{{(3 w^{12} z^{5})}^{3}} \sin c e {(3 w^{12} z^{5})}^{3} = 27 w^{36} z^{15} = 3 w^{12} z^{5}$

Therefore, the solution is $3 w^{12} z^{5}$

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91影视

Simplify: $(a) \sqrt{225 m^{2} n^{2}} (b) \sqrt{169 x^{10} y^{14}} (c) \sqrt[3]{27 w^{36} z^{15}}$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 1. Given information

Part (b) Step 2. Calculation

Part (c) Step 1. Given information

Part (c) Step 2. Calculation

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91影视

Simplify:(a)225m2n2(b)169x10y14(c)27w36z153

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 1. Given information

Part (b) Step 2. Calculation

Part (c) Step 1. Given information

Part (c) Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Probability and Statistics

Calculus

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Simplify: $(a) \sqrt{225 m^{2} n^{2}} (b) \sqrt{169 x^{10} y^{14}} (c) \sqrt[3]{27 w^{36} z^{15}}$