Which option is a rational number between 7 and 8?
Answer and explanation
Correct answer: \(\frac{15}{2}\)
A rational number can be expressed as a ratio of two integers. \(\frac{15}{2}=7.5\) lies between 7 and 8 and is explicitly a ratio of integers, so it is rational. The other choices are irrational: \(\sqrt{53}\) and \(\sqrt{60}\) are square roots of non-perfect squares, and \(\pi+4\) is irrational because \(\pi\) is irrational. The closest distractor is \(\sqrt{53}\) (≈7.2801) but it remains irrational. Exam tip: check if a number can be written as m/n with integers m,n; if not, test for perfect squares or known irrational constants to rule out rationality quickly.
Frequently asked questions
What is the correct answer to this question?
\(\frac{15}{2}\)
Why is this the correct answer?
A rational number can be expressed as a ratio of two integers. \(\frac{15}{2}=7.5\) lies between 7 and 8 and is explicitly a ratio of integers, so it is rational. The other choices are irrational: \(\sqrt{53}\) and \(\sqrt{60}\) are square roots of non-perfect squares, and \(\pi+4\) is irrational because \(\pi\) is irrational. The closest distractor is \(\sqrt{53}\) (≈7.2801) but it remains irrational. Exam tip: check if a number can be written as m/n with integers m,n; if not, test for perfect squares or known irrational constants to rule out rationality quickly.
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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