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,...
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Which of the following numbers is NOT a rational number?
![**Quiz Question: Identifying Rational Numbers**
**Question:**
Which of the following numbers is **NOT** a rational number?
**Options:**
A) \( \sqrt{64} \)
B) \( \sqrt{11} \)
C) \( \frac{1}{7} \)
D) 2.18
E) 0.3
**Explanation:**
- **Rational Numbers** are numbers that can be expressed as a fraction \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \neq 0 \).
- **Option A: \( \sqrt{64} \)** evaluates to 8, which is rational because it can be written as \( \frac{8}{1} \).
- **Option B: \( \sqrt{11} \)** is an irrational number because 11 is not a perfect square.
- **Option C: \( \frac{1}{7} \)** is already in the form of a fraction, hence rational.
- **Option D: 2.18** can be expressed as \( \frac{218}{100} \), making it rational.
- **Option E: 0.3** is equal to \( \frac{3}{10} \), also rational.
**Correct Answer:** **B) \( \sqrt{11} \)** is not a rational number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8296e9ff-1bd6-4a68-b702-8b42b130cc75%2Fbdb6ecd3-6169-4790-93a8-ca3a73579c21%2Fbvokesb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Quiz Question: Identifying Rational Numbers**
**Question:**
Which of the following numbers is **NOT** a rational number?
**Options:**
A) \( \sqrt{64} \)
B) \( \sqrt{11} \)
C) \( \frac{1}{7} \)
D) 2.18
E) 0.3
**Explanation:**
- **Rational Numbers** are numbers that can be expressed as a fraction \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \neq 0 \).
- **Option A: \( \sqrt{64} \)** evaluates to 8, which is rational because it can be written as \( \frac{8}{1} \).
- **Option B: \( \sqrt{11} \)** is an irrational number because 11 is not a perfect square.
- **Option C: \( \frac{1}{7} \)** is already in the form of a fraction, hence rational.
- **Option D: 2.18** can be expressed as \( \frac{218}{100} \), making it rational.
- **Option E: 0.3** is equal to \( \frac{3}{10} \), also rational.
**Correct Answer:** **B) \( \sqrt{11} \)** is not a rational number.
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