If \(a=\sqrt{6}+1\), what type of number is \(a-1\)?
Answer and explanation
Correct answer: Irrational number
\(a-1=\sqrt{6}\). Since 6 is not a perfect square, \(\sqrt{6}\) cannot be written as a ratio \(p/q\) of integers, so it is irrational. Option B (rational) is incorrect because \(\sqrt{6}\) is not expressible as a fraction of integers; options C (integer) and D (zero) are incorrect because \(\sqrt{6}\) is neither an integer nor zero. Exam tip: simplify the expression first and check whether the square root is of a perfect square — if not, it is irrational.
Frequently asked questions
What is the correct answer to this question?
Irrational number
Why is this the correct answer?
\(a-1=\sqrt{6}\). Since 6 is not a perfect square, \(\sqrt{6}\) cannot be written as a ratio \(p/q\) of integers, so it is irrational. Option B (rational) is incorrect because \(\sqrt{6}\) is not expressible as a fraction of integers; options C (integer) and D (zero) are incorrect because \(\sqrt{6}\) is neither an integer nor zero. Exam tip: simplify the expression first and check whether the square root is of a perfect square — if not, it is irrational.
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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