Between which two consecutive integers does \(\sqrt{89}+1\) lie on the number line?
Answer and explanation
Correct answer: 10 and 11
Since \(9^2=81<89<100=10^2\), we get \(9<\sqrt{89}<10\). Adding 1 to all parts gives \(10<\sqrt{89}+1<11\), so the expression lies between 10 and 11. Option A bounds only \(\sqrt{89}\), not the complete expression. Exam tip: compare the number with the nearest consecutive perfect squares to bound a square root.
Frequently asked questions
What is the correct answer to this question?
10 and 11
Why is this the correct answer?
Since \(9^2=81<89<100=10^2\), we get \(9<\sqrt{89}<10\). Adding 1 to all parts gives \(10<\sqrt{89}+1<11\), so the expression lies between 10 and 11. Option A bounds only \(\sqrt{89}\), not the complete expression. Exam tip: compare the number with the nearest consecutive perfect squares to bound a square root.
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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