Chapter 9: Q 9.178. (page 1113)

Simplify a) $\sqrt[3]{- 216}$ b) $\sqrt[4]{- 81}$ c) $\sqrt[5]{- 1024}$

Short Answer

Expert verified

Part (a) $\sqrt[3]{- 216} = - 6$

Part (b) role="math" localid="1649335395335" $\sqrt[4]{- 81} =$ Not a real number.

Part (c) $\sqrt[5]{- 1024} = - 4$

Step by step solution

Part (a) Step 1 : Given Information

The given expression is $\sqrt[3]{- 216}$ .

Part (a) Step 2: Simplification

Using the formula of ${(a^{m})}^{\frac{1}{m}} = a^{m \times \frac{1}{m}}$

localid="1648703874458" $\sqrt[3]{- 216} = {(- 216)}^{\frac{1}{3}} = ({(- 6)}^{3})^{\frac{1}{3}} = {(- 6)}^{3 \times \frac{1}{3}} = - 6$

Hence, $\sqrt[3]{- 216} = - 6$ .

Part (b) Step 1: Given information

The given expression is $\sqrt[4]{- 81}$ .

Part (b) Step 2: Simplification

Simplify $\sqrt[4]{- 81}$ as shown.

No real number raised to the fourth power is positive.

So, it is,

Not a real number.

Part (c) Step 1: Given information

The given expression is $\sqrt[5]{- 1024}$ .

Part (c) Step 2: Simplification

Simplify $\sqrt[5]{- 1024}$ as shown.

localid="1649336555621" $\sqrt[5]{- 1024} = {(- 1024)}^{\frac{1}{5}} = {(- 4^{5})}^{\frac{1}{5}} = - 4$

Hence, localid="1649336659163" $\sqrt[5]{- 1024} = - 4$ .

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) $\sqrt[3]{- 216}$ b) $\sqrt[4]{- 81}$ c) $\sqrt[5]{- 1024}$

Short Answer

Step by step solution

Part (a) Step 1 : Given Information

Part (a) Step 2: Simplification

Part (b) Step 1: Given information

Part (b) Step 2: Simplification

Part (c) Step 1: Given information

Part (c) Step 2: Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify a)-2163b)-814c)-10245

Short Answer

Step by step solution

Part (a) Step 1 : Given Information

Part (a) Step 2: Simplification

Part (b) Step 1: Given information

Part (b) Step 2: Simplification

Part (c) Step 1: Given information

Part (c) Step 2: Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify a) $\sqrt[3]{- 216}$ b) $\sqrt[4]{- 81}$ c) $\sqrt[5]{- 1024}$