Which of the following numbers lies between 3 and 4 and is irrational?
Answer and explanation
Correct answer: \(\sqrt{13}\)
\(\sqrt{13}\) is correct because \(9<13<16\) implies \(3<\sqrt{13}<4\), and 13 is not a perfect square so \(\sqrt{13}\) is irrational. The other choices fail: \(22/7\) and \(7/2\) are ratios of integers (hence rational), and \(\sqrt{16}=4\) is not between 3 and 4. Exam tip: For \(\sqrt{n}\) check whether n lies between two consecutive perfect squares to locate it, and test rationality by seeing if the number can be written as a fraction of integers or is a square root of a non-square integer.
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{13}\)
Why is this the correct answer?
\(\sqrt{13}\) is correct because \(9<13<16\) implies \(3<\sqrt{13}<4\), and 13 is not a perfect square so \(\sqrt{13}\) is irrational. The other choices fail: \(22/7\) and \(7/2\) are ratios of integers (hence rational), and \(\sqrt{16}=4\) is not between 3 and 4. Exam tip: For \(\sqrt{n}\) check whether n lies between two consecutive perfect squares to locate it, and test rationality by seeing if the number can be written as a fraction of integers or is a square root of a non-square integer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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