In number system \(\sqrt{2}\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Irrational number
An irrational number is a real number that cannot be written as \(\frac{p}{q}\) with integers \(p\) and \(q\ne0\); its decimal form never ends and never repeats. The square root of a whole number that is not a perfect square is irrational, and 2 is not a perfect square, so \(\sqrt{2}=1.41421\ldots\) is irrational.
Why the other options are incorrect
Option (1) Rational number — Incorrect. A rational number can be written as \(\frac{p}{q}\); no such fraction squares to 2.
Option (3) Whole number — Incorrect. Whole numbers are 0, 1, 2, 3, ...; \(\sqrt{2}\) lies between 1 and 2.
Option (4) Complex number — Incorrect. A complex number has the form \(a+ib\) with \(i=\sqrt{-1}\); \(\sqrt{2}\) is a real number, with no imaginary part.