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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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