Question

Classify the following numbers as rational or irrational:

(i) 23

(II) 225 

(iii) 0.3796

Answer 1

(i) √23

We know that on finding the square root of √23, we will not get an integer. Therefore, we conclude that 23 is an irrational number.

(ii) √225

We know that on finding the square root of √225, we get 15, which is an integer. Therefore, we conclude that 225 is a rational number.

(iii) √0.3796

We know that 0.3796 can be converted into p/q while, converting 0.3796 into p/q form, we get

0.3796 = 3796/10000 .

The rational number 3796/10000 can be converted into lowest fractions, to get 949/2500

We can observe that 0.3796 can be converted into a rational number. Therefore, we conclude that 0.3796 is a rational number.