17 Which of the following numbers is NOT a rational number? A V64 B C. D 2.18 E 0.3

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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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.
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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