If \(x=\sqrt{11}\), what type of number is \(x^2+1\)?
Answer and explanation
Correct answer: Rational number
Here \(x^2=(\sqrt{11})^2=11\), so \(x^2+1=12\). The number 12 is an integer and can be written as \(12/1\), therefore it is rational. The closest distractor is "irrational", but irrational numbers cannot be expressed as a ratio of integers whereas 12 can; "non-real" is incorrect because 12 is real; "non-repeating decimal" is wrong because 12 has a terminating decimal form (12.0). Exam tip: when you square a square root, the radical cancels first—compute that before classifying the result.
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What is the correct answer to this question?
Rational number
Why is this the correct answer?
Here \(x^2=(\sqrt{11})^2=11\), so \(x^2+1=12\). The number 12 is an integer and can be written as \(12/1\), therefore it is rational. The closest distractor is "irrational", but irrational numbers cannot be expressed as a ratio of integers whereas 12 can; "non-real" is incorrect because 12 is real; "non-repeating decimal" is wrong because 12 has a terminating decimal form (12.0). Exam tip: when you square a square root, the radical cancels first—compute that before classifying the result.
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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