Chapter 8: Q. 8.50 (page 770)

Simplify:
$(a) \frac{\sqrt{128 m^{9}}}{\sqrt{2 m}} (b) \frac{\sqrt[3]{- 192}}{\sqrt[3]{3}} (c) \frac{\sqrt[4]{324 n^{7}}}{\sqrt[4]{2 n^{3}}} .$

Short Answer

Expert verified

Part a. After simplifying we get, $8 m^{4} .$

Part b. After simplifying we get, $- 4 .$

Part c. After simplifying we get, $3 n \sqrt[4]{2} .$

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt{128 m^{9}}}{\sqrt{2 m}}$

By using the property we can write as $\sqrt{\frac{128 m^{9}}{2 m}} .$

Part a Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt{\frac{128 m^{9}}{2 m}} = \sqrt{64 m^{9 - 1}} = \sqrt{{(8 m^{4})}^{2}} = 8 m^{4}$

Part b Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt[3]{- 192}}{\sqrt[3]{3}}$

By using the property we can write as $\sqrt[3]{\frac{- 192}{3}} .$

Part b Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt[3]{\frac{- 192}{3}} = \sqrt[3]{- 64} = \sqrt[3]{- {(4)}^{3}} = - 4$

Part c Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt[4]{324 n^{7}}}{\sqrt[4]{2 n^{3}}}$

By using the property we can write as $\sqrt[4]{\frac{324 n^{7}}{2 n^{3}}} .$

Part c Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt[4]{\frac{324 n^{7}}{2 n^{3}}} = \sqrt[4]{162 n^{7 - 3}} = \sqrt[4]{162 n^{4}} = \sqrt[4]{{(3 n)}^{4}} \cdot \sqrt[4]{2} = 3 n \sqrt[4]{2}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Simplify:
$(a) \frac{\sqrt{128 m^{9}}}{\sqrt{2 m}} (b) \frac{\sqrt[3]{- 192}}{\sqrt[3]{3}} (c) \frac{\sqrt[4]{324 n^{7}}}{\sqrt[4]{2 n^{3}}} .$

Short Answer

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Part a Step 2: Simplify the fraction under the radical

Part b Step 1. Use the Quotient property to write as one radical

Part b Step 2: Simplify the fraction under the radical

Part c Step 1. Use the Quotient property to write as one radical

Part c Step 2: Simplify the fraction under the radical

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Pure Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:a128m92mb-192333c324n742n34.

Short Answer

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Part a Step 2: Simplify the fraction under the radical

Part b Step 1. Use the Quotient property to write as one radical

Part b Step 2: Simplify the fraction under the radical

Part c Step 1. Use the Quotient property to write as one radical

Part c Step 2: Simplify the fraction under the radical

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Pure Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \frac{\sqrt{128 m^{9}}}{\sqrt{2 m}} (b) \frac{\sqrt[3]{- 192}}{\sqrt[3]{3}} (c) \frac{\sqrt[4]{324 n^{7}}}{\sqrt[4]{2 n^{3}}} .$