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The value of √2 lies between:
- a)1.3 and 1.4
- b)1.41 and 1.42
- c)1.5 and 1.6
- d)1.2 and 1.3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The value of √2 lies between:a)1.3 and 1.4b)1.41 and 1.42c)1.5 and 1.6...
Square the endpoints to locate √2.
1.412 = 1.9881 < 2.
1.422 = 2.0164 > 2.
Therefore √2 lies between 1.41 and 1.42.
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The value of √2 lies between:a)1.3 and 1.4b)1.41 and 1.42c)1.5 and 1.6...
Understanding the Value of √2
To determine the value of √2, we can use approximation and estimation techniques.
Finding the Range for √2
- We know that √1 = 1 and √4 = 2.
- Therefore, √2 must lie between 1 and 2.
Estimation Between 1.4 and 1.5
- Let's check the squares of 1.4 and 1.5:
- 1.4 x 1.4 = 1.96
- 1.5 x 1.5 = 2.25
- Since 1.96 is less than 2 and 2.25 is more than 2, this confirms that √2 lies between 1.4 and 1.5.
Refining the Estimate
- Now, we can narrow the range further by checking 1.41 and 1.42:
- 1.41 x 1.41 = 1.9881
- 1.42 x 1.42 = 2.0164
- Here, 1.9881 is less than 2, and 2.0164 is more than 2. Thus, √2 is between 1.41 and 1.42.
Conclusion
- The correct answer is option 'B': √2 lies between 1.41 and 1.42.
- This confirms that the value of √2 is approximately 1.414, making it a very precise estimate.
By using these calculations, we can confidently determine the approximate value of √2 and understand its range better.
To determine the value of √2, we can use approximation and estimation techniques.
Finding the Range for √2
- We know that √1 = 1 and √4 = 2.
- Therefore, √2 must lie between 1 and 2.
Estimation Between 1.4 and 1.5
- Let's check the squares of 1.4 and 1.5:
- 1.4 x 1.4 = 1.96
- 1.5 x 1.5 = 2.25
- Since 1.96 is less than 2 and 2.25 is more than 2, this confirms that √2 lies between 1.4 and 1.5.
Refining the Estimate
- Now, we can narrow the range further by checking 1.41 and 1.42:
- 1.41 x 1.41 = 1.9881
- 1.42 x 1.42 = 2.0164
- Here, 1.9881 is less than 2, and 2.0164 is more than 2. Thus, √2 is between 1.41 and 1.42.
Conclusion
- The correct answer is option 'B': √2 lies between 1.41 and 1.42.
- This confirms that the value of √2 is approximately 1.414, making it a very precise estimate.
By using these calculations, we can confidently determine the approximate value of √2 and understand its range better.
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The value of √2 lies between:a)1.3 and 1.4b)1.41 and 1.42c)1.5 and 1.6d)1.2 and 1.3Correct answer is option 'B'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The value of √2 lies between:a)1.3 and 1.4b)1.41 and 1.42c)1.5 and 1.6d)1.2 and 1.3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of √2 lies between:a)1.3 and 1.4b)1.41 and 1.42c)1.5 and 1.6d)1.2 and 1.3Correct answer is option 'B'. Can you explain this answer?.
The value of √2 lies between:a)1.3 and 1.4b)1.41 and 1.42c)1.5 and 1.6d)1.2 and 1.3Correct answer is option 'B'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The value of √2 lies between:a)1.3 and 1.4b)1.41 and 1.42c)1.5 and 1.6d)1.2 and 1.3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of √2 lies between:a)1.3 and 1.4b)1.41 and 1.42c)1.5 and 1.6d)1.2 and 1.3Correct answer is option 'B'. Can you explain this answer?.
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