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.