Classify the following numbers as rational or irrational : (i) root of 23 (ii)root of 225 (iii)0.3796 (iv)7.478478.. (v)1.101001000100001...

(i) 23

√23 = 4.795831523…

Since the decimal expansion is non-terminating and nonrecurring. Therefore, √23 is an irrational number.

(ii) 225

225 = 15

Therefore, 225 is a rational number.

(iii) 0.3796

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.

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