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Which of the following is not an irrational number
a) 7√5
c) (√7 – 3) -
b) 2√2 + 2
d) 2√3 + 2?
a) 7√5
c) (√7 – 3) -
b) 2√2 + 2
d) 2√3 + 2?
Most Upvoted Answer
Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - ...
Understanding Irrational Numbers
Irrational numbers are real numbers that cannot be expressed as a fraction of two integers. They have non-repeating and non-terminating decimal expansions. Let's analyze the given options to identify which one is not an irrational number.
Option Analysis
- a) 7√5
- The square root of 5 is irrational.
- Multiplying an irrational number by a rational number (7) remains irrational.
- Therefore, 7√5 is irrational.
- b) 2√2 + 2
- The square root of 2 is irrational.
- When multiplied by 2, it remains irrational (2√2).
- Adding 2 (a rational number) to an irrational number (2√2) results in an irrational number.
- Thus, 2√2 + 2 is irrational.
- c) (√7 - 3)
- The square root of 7 is irrational.
- Subtracting a rational number (3) from an irrational number (√7) keeps the result irrational.
- Therefore, (√7 - 3) is irrational.
- d) 2√3 + 2
- The square root of 3 is irrational.
- Multiplying by 2 gives 2√3, which is irrational.
- Adding 2 (a rational number) to an irrational number (2√3) results in an irrational number.
- Thus, 2√3 + 2 is irrational.
Conclusion
All options a), b), c), and d) are irrational numbers. However, if we were to evaluate the entire expression in option b), we find that it can be rewritten as a decimal approximation, which could suggest rationality under certain conditions. Nonetheless, all choices involve irrational components.
Since the question asks for one that is not, it is important to note that all provided answers are indeed irrational numbers.
Irrational numbers are real numbers that cannot be expressed as a fraction of two integers. They have non-repeating and non-terminating decimal expansions. Let's analyze the given options to identify which one is not an irrational number.
Option Analysis
- a) 7√5
- The square root of 5 is irrational.
- Multiplying an irrational number by a rational number (7) remains irrational.
- Therefore, 7√5 is irrational.
- b) 2√2 + 2
- The square root of 2 is irrational.
- When multiplied by 2, it remains irrational (2√2).
- Adding 2 (a rational number) to an irrational number (2√2) results in an irrational number.
- Thus, 2√2 + 2 is irrational.
- c) (√7 - 3)
- The square root of 7 is irrational.
- Subtracting a rational number (3) from an irrational number (√7) keeps the result irrational.
- Therefore, (√7 - 3) is irrational.
- d) 2√3 + 2
- The square root of 3 is irrational.
- Multiplying by 2 gives 2√3, which is irrational.
- Adding 2 (a rational number) to an irrational number (2√3) results in an irrational number.
- Thus, 2√3 + 2 is irrational.
Conclusion
All options a), b), c), and d) are irrational numbers. However, if we were to evaluate the entire expression in option b), we find that it can be rewritten as a decimal approximation, which could suggest rationality under certain conditions. Nonetheless, all choices involve irrational components.
Since the question asks for one that is not, it is important to note that all provided answers are indeed irrational numbers.
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Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - b) 2√2 + 2d) 2√3 + 2?
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Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - b) 2√2 + 2d) 2√3 + 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - b) 2√2 + 2d) 2√3 + 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - b) 2√2 + 2d) 2√3 + 2?.
Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - b) 2√2 + 2d) 2√3 + 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - b) 2√2 + 2d) 2√3 + 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - b) 2√2 + 2d) 2√3 + 2?.
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