In a number system \(\sqrt{3}\) 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 \(q\ne0\). The square root of a whole number that is not a perfect square is irrational, and 3 is not a perfect square, so \(\sqrt{3}=1.7320508\ldots\) never ends or repeats.
Why the other options are incorrect
Option (1) Complex number — Incorrect. Every real number is a complex number \(a+bi\) with \(b=0\), but \(\sqrt{3}\) has no imaginary part, so its exact type is irrational.
Option (3) Rational number — Incorrect. A rational number can be written as \(\frac{p}{q}\); no fraction equals \(\sqrt{3}\).
Option (4) Whole number — Incorrect. \(\sqrt{3}\) lies between 1 and 2, so it is not one of 0, 1, 2, 3, ...