Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Question:** Which number is an irrational number? **Options:** - ○ \(-10\) - ○ \(-\sqrt{9}\) - ○ \(\sqrt{17}\) - ○ \(5,499\) **Explanation:** The question requires you to identify which number among the given options is irrational. An irrational number is a number that cannot be expressed as a simple fraction, meaning it has a non-repeating, non-terminating decimal expansion. ### Detailed Explanation of Options: 1. **\(-10\)**: This is a rational number because it can be expressed as \(\frac{-10}{1}\), which is a simple fraction. 2. **\(-\sqrt{9}\)**: The square root of 9 is 3, thus \(-\sqrt{9}\) simplifies to \(-3\), which is rational because it can be expressed as \(\frac{-3}{1}\). 3. **\(\sqrt{17}\)**: The square root of 17 does not simplify to a whole number and cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion, making it an irrational number. 4. **\(5,499\)**: This is a rational number because it can be expressed as \(\frac{5,499}{1}\), which is a simple fraction. ### Conclusion: The number \(\sqrt{17}\) is the irrational number.
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Transcribed Image Text:**Question:** Which number is an irrational number? **Options:** - ○ \(-10\) - ○ \(-\sqrt{9}\) - ○ \(\sqrt{17}\) - ○ \(5,499\) **Explanation:** The question requires you to identify which number among the given options is irrational. An irrational number is a number that cannot be expressed as a simple fraction, meaning it has a non-repeating, non-terminating decimal expansion. ### Detailed Explanation of Options: 1. **\(-10\)**: This is a rational number because it can be expressed as \(\frac{-10}{1}\), which is a simple fraction. 2. **\(-\sqrt{9}\)**: The square root of 9 is 3, thus \(-\sqrt{9}\) simplifies to \(-3\), which is rational because it can be expressed as \(\frac{-3}{1}\). 3. **\(\sqrt{17}\)**: The square root of 17 does not simplify to a whole number and cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion, making it an irrational number. 4. **\(5,499\)**: This is a rational number because it can be expressed as \(\frac{5,499}{1}\), which is a simple fraction. ### Conclusion: The number \(\sqrt{17}\) is the irrational number.
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