Question

Classify the following numbers as rational or irrational.
(i) $\sqrt{11}$
(ii) $\sqrt{81}$
(iii) $0.0625$
(iv) $0.8\overline{3}$
(v) $1.505500555$....

Answer 1

(i) $\sqrt{11}$ is an irrational number.($11$ is not a perfect square number)
(ii) $\sqrt{81}=9=\frac{9}{1}$, a rational number.
(iii) $0.0625$ is a terminating decimal.
$\therefore 0.0625$ is a rational number.
(iv) $0.8\overline{3}=0.8333$...
The decimal expansion is non-terminating and recurring.
$\therefore 0.8\overline{3}$ is a rational number.
(v) The decimal number is non-terminating and non-recurring.
$\therefore 1.505500555$.... is an irrational number.