A student claims that V80 is in the simplest radical form. Which statement is true? The claim is incorrect because 80 has a factor of 4. O The claim is correct because 80 is not divisible by three. The claim is incorrect because 80 has a factor of 8. The claim is correct because 80 is not a perfect cube.
A student claims that V80 is in the simplest radical form. Which statement is true? The claim is incorrect because 80 has a factor of 4. O The claim is correct because 80 is not divisible by three. The claim is incorrect because 80 has a factor of 8. The claim is correct because 80 is not a perfect cube.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![### Simplifying Radical Expressions
A student claims that \( \sqrt[3]{80} \) is in the simplest radical form. Which statement is true?
- ⃝ The claim is incorrect because 80 has a factor of 4.
- ⃝ The claim is correct because 80 is not divisible by three.
- ⃝ The claim is incorrect because 80 has a factor of 8.
- ⃝ The claim is correct because 80 is not a perfect cube.
In evaluating the given radical expression \( \sqrt[3]{80} \), consider the factors of 80 to determine if it is already in its simplest form or can be simplified further.
### Understanding Cube Roots
A cube root is simplified when the radicand (the number under the radical sign) has no perfect cube factors other than 1.
#### Step-by-Step Analysis:
1. **Factor 80**:
\[
80 = 2^4 \cdot 5
\]
2. **Identify Perfect Cubes**:
- \( 2^3 = 8 \) is a perfect cube and is a factor of 80.
3. **Simplify**:
- \( \sqrt[3]{80} = \sqrt[3]{2^4 \cdot 5} = \sqrt[3]{8 \cdot 10} = \sqrt[3]{8} \cdot \sqrt[3]{10} = 2 \cdot \sqrt[3]{10} \)
The simplified form of \( \sqrt[3]{80} \) is \( 2 \cdot \sqrt[3]{10} \).
### Conclusion:
The correct statement is that the claim is incorrect because 80 has a factor of 8, making the third option the true statement.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1246267-81e7-461b-97b7-8e9aaefad2fd%2Fb1842d63-3169-47e7-9cee-9eb1620e226c%2Fswe0aau_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Simplifying Radical Expressions
A student claims that \( \sqrt[3]{80} \) is in the simplest radical form. Which statement is true?
- ⃝ The claim is incorrect because 80 has a factor of 4.
- ⃝ The claim is correct because 80 is not divisible by three.
- ⃝ The claim is incorrect because 80 has a factor of 8.
- ⃝ The claim is correct because 80 is not a perfect cube.
In evaluating the given radical expression \( \sqrt[3]{80} \), consider the factors of 80 to determine if it is already in its simplest form or can be simplified further.
### Understanding Cube Roots
A cube root is simplified when the radicand (the number under the radical sign) has no perfect cube factors other than 1.
#### Step-by-Step Analysis:
1. **Factor 80**:
\[
80 = 2^4 \cdot 5
\]
2. **Identify Perfect Cubes**:
- \( 2^3 = 8 \) is a perfect cube and is a factor of 80.
3. **Simplify**:
- \( \sqrt[3]{80} = \sqrt[3]{2^4 \cdot 5} = \sqrt[3]{8 \cdot 10} = \sqrt[3]{8} \cdot \sqrt[3]{10} = 2 \cdot \sqrt[3]{10} \)
The simplified form of \( \sqrt[3]{80} \) is \( 2 \cdot \sqrt[3]{10} \).
### Conclusion:
The correct statement is that the claim is incorrect because 80 has a factor of 8, making the third option the true statement.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education