If \(m\) is an integer such that \(m<\sqrt{57}<m+1\), what is the value of \(m\)?
Answer and explanation
Correct answer: 7
Since \(7^2=49<57<64=8^2\), we have \(7<\sqrt{57}<8\). Comparing this with \(m<\sqrt{57}<m+1\) gives \(m=7\). Option 6 is too small because \(6^2=36<57\), while 8 is an upper bound, not the required integer. Exam tip: locate a square root between two consecutive perfect squares to find its integer part.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Since \(7^2=49<57<64=8^2\), we have \(7<\sqrt{57}<8\). Comparing this with \(m<\sqrt{57}<m+1\) gives \(m=7\). Option 6 is too small because \(6^2=36<57\), while 8 is an upper bound, not the required integer. Exam tip: locate a square root between two consecutive perfect squares to find its integer part.
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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