If \(\sqrt{n}\) lies between \(7.2\) and \(7.3\) on the number line, which value of \(n\) is possible?
Answer and explanation
Correct answer: \(52\)
Since \(7.2<\sqrt{n}<7.3\) and both boundary values are positive, squaring gives \(7.2^2<n<7.3^2\). Thus, \(51.84<n<53.29\). Only \(52\) lies in this interval; \(51\) and \(50\) are too small, while \(54\) is too large. Exam tip: when both sides of an inequality are positive, squaring preserves its direction.
Frequently asked questions
What is the correct answer to this question?
\(52\)
Why is this the correct answer?
Since \(7.2<\sqrt{n}<7.3\) and both boundary values are positive, squaring gives \(7.2^2<n<7.3^2\). Thus, \(51.84<n<53.29\). Only \(52\) lies in this interval; \(51\) and \(50\) are too small, while \(54\) is too large. Exam tip: when both sides of an inequality are positive, squaring preserves its direction.
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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