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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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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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

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

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