If m is an integer and \(m<\sqrt{145}<m+1\), what is the value of m?
Answer and explanation
Correct answer: 12
Since \(12^2=144<145<169=13^2\), we get \(12<\sqrt{145}<13\). Comparing this with \(m<\sqrt{145}<m+1\) gives \(m=12\). Option 13 is incorrect because \(\sqrt{145}<13\), so \(13<\sqrt{145}\) is not true. Exam tip: the integer part of a square root is the greatest integer whose square is less than or equal to the given number.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Since \(12^2=144<145<169=13^2\), we get \(12<\sqrt{145}<13\). Comparing this with \(m<\sqrt{145}<m+1\) gives \(m=12\). Option 13 is incorrect because \(\sqrt{145}<13\), so \(13<\sqrt{145}\) is not true. Exam tip: the integer part of a square root is the greatest integer whose square is less than or equal to 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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