If \(\sqrt{n}\) lies between 6.4 and 6.5 on the number line, which value of \(n\) can be correct?
Answer and explanation
Correct answer: 42
Since \(6.4<\sqrt{n}<6.5\), squaring both sides gives \(6.4^2<n<6.5^2\). Therefore, \(40.96<n<42.25\). Among the given choices, only 42 lies in this interval. The values 40, 45 and 49 fall outside it. Exam tip: for positive quantities, squaring preserves the direction of the inequality.
Frequently asked questions
What is the correct answer to this question?
42
Why is this the correct answer?
Since \(6.4<\sqrt{n}<6.5\), squaring both sides gives \(6.4^2<n<6.5^2\). Therefore, \(40.96<n<42.25\). Among the given choices, only 42 lies in this interval. The values 40, 45 and 49 fall outside it. Exam tip: for positive quantities, squaring preserves the direction of the 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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