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Which of the following is not an irrational number
a) 7√5
c) (√7 – 3) - root 7
b) 2√2 + 2
d) 2√3 + 2.
correct answer is (c) explain why?
a) 7√5
c) (√7 – 3) - root 7
b) 2√2 + 2
d) 2√3 + 2.
correct answer is (c) explain why?
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, non-terminating decimal expansions. Let's analyze the options provided to identify which one is not an irrational number.
Option Analysis
- a) 7√5
The square root of 5 is irrational, and multiplying it by 7 (a rational number) results in an irrational number. Thus, 7√5 is irrational.
- b) 2√2 + 2
√2 is irrational, and when multiplied by 2, it remains irrational. Adding 2 (a rational number) to an irrational number still yields an irrational result. Therefore, 2√2 + 2 is irrational.
- c) (√7 – 3) - root 7
Here, √7 is irrational. However, when we simplify the expression, we get:
(√7 - 3) - √7 = -3.
-3 is a rational number because it can be expressed as -3/1. Hence, this option is not irrational.
- d) 2√3 + 2
Similar to the previous options, 2√3 is irrational, and adding 2 keeps it irrational. Therefore, 2√3 + 2 is irrational.
Conclusion
The correct answer is (c) (√7 – 3) - root 7, as it simplifies to -3, a rational number. This explanation highlights the importance of recognizing how operations with rational and irrational numbers affect their classifications.
Irrational numbers are real numbers that cannot be expressed as a fraction of two integers. They have non-repeating, non-terminating decimal expansions. Let's analyze the options provided to identify which one is not an irrational number.
Option Analysis
- a) 7√5
The square root of 5 is irrational, and multiplying it by 7 (a rational number) results in an irrational number. Thus, 7√5 is irrational.
- b) 2√2 + 2
√2 is irrational, and when multiplied by 2, it remains irrational. Adding 2 (a rational number) to an irrational number still yields an irrational result. Therefore, 2√2 + 2 is irrational.
- c) (√7 – 3) - root 7
Here, √7 is irrational. However, when we simplify the expression, we get:
(√7 - 3) - √7 = -3.
-3 is a rational number because it can be expressed as -3/1. Hence, this option is not irrational.
- d) 2√3 + 2
Similar to the previous options, 2√3 is irrational, and adding 2 keeps it irrational. Therefore, 2√3 + 2 is irrational.
Conclusion
The correct answer is (c) (√7 – 3) - root 7, as it simplifies to -3, a rational number. This explanation highlights the importance of recognizing how operations with rational and irrational numbers affect their classifications.
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Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - root 7b) 2√2 + 2d) 2√3 + 2. correct answer is (c) explain why?
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Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - root 7b) 2√2 + 2d) 2√3 + 2. correct answer is (c) explain why? 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) - root 7b) 2√2 + 2d) 2√3 + 2. correct answer is (c) explain why? 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) - root 7b) 2√2 + 2d) 2√3 + 2. correct answer is (c) explain why?.
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