Chapter 11: Q. 8.36 (page 1069)

Simplify:
$(a) \sqrt[3]{- 625} (b) \sqrt[4]{- 324} .$

Short Answer

Expert verified

Part a. After simplifying we get, $- 5 \sqrt[3]{5} .$

Part b. After simplifying we get, $3 \sqrt[4]{- 4} .$

Step by step solution

Part a Step 1. Rewrite the radicand as a product using perfect cube factors

So, $\sqrt[3]{- 625} = \sqrt[3]{{(- 5)}^{3} 5}$

Part a Step 2. Take the cube root

By taking the cube root we get,

$= - 5 \sqrt[3]{5}$

Part b Step 1. Rewrite the radicand as a product using the largest perfect cube factor

So,

$\sqrt[4]{- 324} = \sqrt[4]{{- (3)}^{4} 2^{2}}$

Part b Step 2. Take the quad root

By taking the quad root we get,

$= \sqrt[4]{- {(3)}^{4} 2^{2}} = 3 \sqrt[4]{- 4}$

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:
$(a) \sqrt[3]{- 625} (b) \sqrt[4]{- 324} .$

Short Answer

Step by step solution

Part a Step 1. Rewrite the radicand as a product using perfect cube factors

Part a Step 2. Take the cube root

Part b Step 1. Rewrite the radicand as a product using the largest perfect cube factor

Part b Step 2. Take the quad root

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify:a-6253b-3244.

Short Answer

Step by step solution

Part a Step 1. Rewrite the radicand as a product using perfect cube factors

Part a Step 2. Take the cube root

Part b Step 1. Rewrite the radicand as a product using the largest perfect cube factor

Part b Step 2. Take the quad root

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \sqrt[3]{- 625} (b) \sqrt[4]{- 324} .$