√23 = 4.795831523…
Since the decimal expansion is non-terminating and nonrecurring. Therefore, √23 is an irrational number.
√225 = 15
Therefore, √225 is a rational number.
0.3796 is a terminating decimal, therefore, it is a rational number.
7.478478… is repeating and non-terminating, therefore it is a rational number.
The given decimal form is non-terminating and non-repeating, therefore it is an irrational number.