If \\(\sqrt{n}\\) lies between 9 and 10 on the number line, which value of n is possible?
Answer and explanation
Correct answer: 91
We have \\(9<\sqrt{n}<10\\). Since both bounds are positive, squaring gives \\(81<n<100\\). The value 91 lies in this interval, so it is possible. The closest distractor is 100, but it is an endpoint and does not satisfy the condition that \\(\sqrt{n}<10\\). Exam tip: when squaring an inequality whose quantities are positive, the inequality signs remain unchanged.
Frequently asked questions
What is the correct answer to this question?
91
Why is this the correct answer?
We have \\(9<\sqrt{n}<10\\). Since both bounds are positive, squaring gives \\(81<n<100\\). The value 91 lies in this interval, so it is possible. The closest distractor is 100, but it is an endpoint and does not satisfy the condition that \\(\sqrt{n}<10\\). Exam tip: when squaring an inequality whose quantities are positive, the inequality signs remain unchanged.
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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