Between which two consecutive integers does \(\sqrt{40}-2\) lie on the number line?
Answer and explanation
Correct answer: 4 and 5
Since \(6^2=36<40<49=7^2\), we get \(6<\sqrt{40}<7\). Subtracting 2 from all parts gives \(4<\sqrt{40}-2<5\), so the number lies between 4 and 5. Option A is incorrect because the value is greater than 4. Exam tip: bound the square root using consecutive perfect squares, then apply the operation to the entire inequality.
Frequently asked questions
What is the correct answer to this question?
4 and 5
Why is this the correct answer?
Since \(6^2=36<40<49=7^2\), we get \(6<\sqrt{40}<7\). Subtracting 2 from all parts gives \(4<\sqrt{40}-2<5\), so the number lies between 4 and 5. Option A is incorrect because the value is greater than 4. Exam tip: bound the square root using consecutive perfect squares, then apply the operation to the entire inequality.
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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