If x lies between 2.6 and 2.7, which test is correct for x = √7?
Answer and explanation
Correct answer: 2.6² < 7 < 2.7²
The governing concept is order preservation when squaring positive numbers. Since both 2.6 and 2.7 are positive, the statement 2.6 < √7 < 2.7 is equivalent to 2.6² < 7 < 2.7². Calculate the endpoint squares: 2.6² = 6.76 and 2.7² = 7.29. Because 6.76 < 7 < 7.29, the required test is true, and √7 does lie in that interval; numerically it is about 2.646. Therefore option A is correct. Option B reverses the natural order of the endpoint squares. Option C says 7 is below the lower square, and option D says it is above the upper square; both contradict the actual inequalities and fail to establish that √7 lies between the given bounds.
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What is the correct answer to this question?
2.6² < 7 < 2.7²
Why is this the correct answer?
The governing concept is order preservation when squaring positive numbers. Since both 2.6 and 2.7 are positive, the statement 2.6 < √7 < 2.7 is equivalent to 2.6² < 7 < 2.7². Calculate the endpoint squares: 2.6² = 6.76 and 2.7² = 7.29. Because 6.76 < 7 < 7.29, the required test is true, and √7 does lie in that interval; numerically it is about 2.646. Therefore option A is correct. Option B reverses the natural order of the endpoint squares. Option C says 7 is below the lower square, and option D says it is above the upper square; both contradict the actual inequalities and fail to establish that √7 lies between the given bounds.
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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