Which option gives the correct decimal bound for \(\sqrt{24}\) on the number line?
Answer and explanation
Correct answer: \(4.8<\sqrt{24}<4.9\)
Since \(4.8^2=23.04\) and \(4.9^2=24.01\), and \(23.04<24<24.01\), it follows that \(4.8<\sqrt{24}<4.9\). Options B and D give intervals that are too small, while both endpoints in option C have squares greater than 24. Exam tip: To verify a decimal bound for a square root, compare the squares of its endpoints with the given number.
Frequently asked questions
What is the correct answer to this question?
\(4.8<\sqrt{24}<4.9\)
Why is this the correct answer?
Since \(4.8^2=23.04\) and \(4.9^2=24.01\), and \(23.04<24<24.01\), it follows that \(4.8<\sqrt{24}<4.9\). Options B and D give intervals that are too small, while both endpoints in option C have squares greater than 24. Exam tip: To verify a decimal bound for a square root, compare the squares of its endpoints with the given number.
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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