Between which two consecutive integers is \(\sqrt{52}\) located on the number line?
Answer and explanation
Correct answer: 7 and 8
Compare the nearest perfect squares: \(7^2=49\) and \(8^2=64\). Since \(49<52<64\), taking square roots gives \(7<\sqrt{52}<8\). Therefore, \(\sqrt{52}\) lies between 7 and 8. Exam tip: To bound a square root, identify the consecutive perfect squares immediately below and above the number.
Frequently asked questions
What is the correct answer to this question?
7 and 8
Why is this the correct answer?
Compare the nearest perfect squares: \(7^2=49\) and \(8^2=64\). Since \(49<52<64\), taking square roots gives \(7<\sqrt{52}<8\). Therefore, \(\sqrt{52}\) lies between 7 and 8. Exam tip: To bound a square root, identify the consecutive perfect squares immediately below and above the 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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