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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?
a) 7√5
c) (√7 – 3) - root 7
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 numbers that cannot be expressed as a fraction of two integers. Their decimal expansions are non-repeating and non-terminating. Let's analyze each option to identify which one is not an irrational number.
Option Analysis
- a) 7√5
- This expression involves the square root of 5, which is irrational. Multiplying an irrational number (√5) by a rational number (7) results in an irrational number. Thus, 7√5 is irrational.
- b) 2√2 + 2
- Here, 2 is a rational number and 2√2 is irrational (since √2 is irrational). The sum of a rational and an irrational number is irrational. Therefore, 2√2 + 2 is also irrational.
- c) (√7 – 3) - root 7
- This expression simplifies to -2√7 - 3. Since √7 is irrational, any linear combination of irrational numbers remains irrational. Hence, (√7 - 3) - √7 is irrational.
- d) 2√3 + 2
- Similar to option b, this expression consists of a rational number (2) and an irrational number (2√3). Their sum is irrational. So, 2√3 + 2 is also irrational.
Conclusion
Upon reviewing all options, it's clear that all provided expressions are irrational numbers. However, if we consider a mistake in interpretation, we may alternatively analyze if any option could represent a rational number.
In this context, all options are irrational, confirming that there are no rational numbers among them.
Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Their decimal expansions are non-repeating and non-terminating. Let's analyze each option to identify which one is not an irrational number.
Option Analysis
- a) 7√5
- This expression involves the square root of 5, which is irrational. Multiplying an irrational number (√5) by a rational number (7) results in an irrational number. Thus, 7√5 is irrational.
- b) 2√2 + 2
- Here, 2 is a rational number and 2√2 is irrational (since √2 is irrational). The sum of a rational and an irrational number is irrational. Therefore, 2√2 + 2 is also irrational.
- c) (√7 – 3) - root 7
- This expression simplifies to -2√7 - 3. Since √7 is irrational, any linear combination of irrational numbers remains irrational. Hence, (√7 - 3) - √7 is irrational.
- d) 2√3 + 2
- Similar to option b, this expression consists of a rational number (2) and an irrational number (2√3). Their sum is irrational. So, 2√3 + 2 is also irrational.
Conclusion
Upon reviewing all options, it's clear that all provided expressions are irrational numbers. However, if we consider a mistake in interpretation, we may alternatively analyze if any option could represent a rational number.
In this context, all options are irrational, confirming that there are no rational numbers among them.
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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?
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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? 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? 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?.
Which of the following is not an irrational numbera) 7√5c) (√7 – 3) - root 7b) 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) - root 7b) 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) - root 7b) 2√2 + 2d) 2√3 + 2?.
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