If \(b\) is an irrational number, what type of number is \(b+0\)?
Answer and explanation
Correct answer: Irrational number
Adding 0 does not change a number — 0 is the additive identity, so \(b+0=b\). Since \(b\) is given as irrational, it remains irrational after adding 0. Option B is wrong because it assumes \(b\) is rational, contrary to the premise; C and D are incorrect because integers are a subset of rationals and "always zero" would require \(b=0\), but 0 is rational, not irrational. Exam tip: remember the additive identity (0) — adding 0 leaves any number unchanged.
Frequently asked questions
What is the correct answer to this question?
Irrational number
Why is this the correct answer?
Adding 0 does not change a number — 0 is the additive identity, so \(b+0=b\). Since \(b\) is given as irrational, it remains irrational after adding 0. Option B is wrong because it assumes \(b\) is rational, contrary to the premise; C and D are incorrect because integers are a subset of rationals and "always zero" would require \(b=0\), but 0 is rational, not irrational. Exam tip: remember the additive identity (0) — adding 0 leaves any number unchanged.
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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