In number system 3√2 , is?

The correct answer is Option (2) → Irrational number

An irrational number cannot be written as \(\frac{p}{q}\) with integers \(p\) and \(q\ne0\); its decimal form never ends and never repeats. Since 2 is not a perfect square, \(\sqrt{2}=1.4142\ldots\) is irrational.

Multiplying an irrational number by a non-zero rational number keeps it irrational: if \(3\sqrt{2}\) were equal to \(\frac{p}{q}\), then \(\sqrt{2}\) would be \(\frac{p}{3q}\), a rational number, which is impossible. So \(3\sqrt{2}=4.2426\ldots\) is irrational, and therefore also not a natural or a whole number.