Question

Classify the following numbers as rational or irrational : 

(i) \(\sqrt23 \)

(ii) \(\sqrt225 \)

(iii) 0.3796 

(iv) 7.478478... 

(v) 1.101001000100001...

Answer 1

(i) \(\sqrt23\) = 4.79583152331.... As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number.

(ii) \(\sqrt225\) = 15= \(\frac{15}{1}\)It is a rational number as it can be represented in \(\frac{p}{q}\) form.

(iii) 0.3796 As the decimal expansion of this number is terminating, therefore, it is a rational number.

(iv) 7.478478 … = \(\overline{7.478 }\) As the decimal expansion of this number is non-terminating recurring, therefore, it is a rational number.

(v) 1.10100100010000 … As the decimal expansion of this number is non-terminating non-repeating, therefore, it is an irrational number.