The smallest natural number which on multiplying with 48 gives a perfect square number is:

1. 12

2. 3

3. $\dfrac{1}{3}$

4. none of the above

Finding prime factors of 48

48 = (2 x 2) x (2 x 2) x 3

Since the prime factor 3 is not in pair.

The given number should be multiplied by 3.

Hence, option 2 is the correct option.