Which decimal value is closest to √199 on the number line?
Answer and explanation
Correct answer: 14.10
Estimate the square root by locating 199 between nearby perfect squares. Since 14² = 196 and 15² = 225, √199 lies just above 14. A more precise estimate is √199 ≈ 14.1067, because 14.1² = 198.81, which is very close to 199. The distance from 14.10 is about 0.0067, much smaller than the distances from 14.35, 13.90, or 14.90. Therefore option A is closest. The other choices are respectively about 0.24, 0.21, and 0.79 away from the root. The key concept is numerical approximation: compare the candidate’s distance from the irrational value rather than merely choosing a nearby-looking number.
Frequently asked questions
What is the correct answer to this question?
14.10
Why is this the correct answer?
Estimate the square root by locating 199 between nearby perfect squares. Since 14² = 196 and 15² = 225, √199 lies just above 14. A more precise estimate is √199 ≈ 14.1067, because 14.1² = 198.81, which is very close to 199. The distance from 14.10 is about 0.0067, much smaller than the distances from 14.35, 13.90, or 14.90. Therefore option A is closest. The other choices are respectively about 0.24, 0.21, and 0.79 away from the root. The key concept is numerical approximation: compare the candidate’s distance from the irrational value rather than merely choosing a nearby-looking number.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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