Between which two consecutive integers does \(\sqrt{131}+2\) lie on the number line?
Answer and explanation
Correct answer: 13 and 14
Since \(11^2=121<131<144=12^2\), we have \(11<\sqrt{131}<12\). Adding 2 to all parts gives \(13<\sqrt{131}+2<14\), so the expression lies between 13 and 14. Option A is incorrect because it corresponds to the bounds of \(\sqrt{131}\), not of the complete expression. Exam tip: compare the number under the square root with the nearest consecutive perfect squares.
Frequently asked questions
What is the correct answer to this question?
13 and 14
Why is this the correct answer?
Since \(11^2=121<131<144=12^2\), we have \(11<\sqrt{131}<12\). Adding 2 to all parts gives \(13<\sqrt{131}+2<14\), so the expression lies between 13 and 14. Option A is incorrect because it corresponds to the bounds of \(\sqrt{131}\), not of the complete expression. Exam tip: compare the number under the square root with the nearest consecutive perfect squares.
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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