In number system 3√2, is?

The correct answer is Option (2) → Irrational number

√2 cannot be written as a ratio of two integers, and multiplying an irrational number by a non-zero rational number leaves it irrational. So 3√2, which is about 4.2426…, is an irrational number.

Its decimal expansion neither terminates nor repeats, which also rules out its being a natural or a whole number.