Question

Classify the following numbers as rational or irrational:
(i) $\sqrt{23}$
(ii) $\sqrt{225}$
(iii) $0.3796$
(iv) $\mathrm{7.478478...}$
(v) $\mathrm{1.101001000100001...}$

Answer 1

Solve the given expressions

(1) $\sqrt{23}=\mathrm{4.795831523..........}$

The decimal expansion is non terminating non recurring.

$\therefore \sqrt{23}$ is a irrational number.

(2)$\sqrt{225}=15$

$\therefore \sqrt{225}$ is a rational number.

(3) $0.3796$ is the decimal expansion is terminating.

So $0.3796$ is a rational number.

(4) $\mathrm{7.478478......}=7.\overline{478}$ is the decimal expansion is non termination and recurring.

$\mathrm{7.478478......}$ is a rational number.

(5) $\mathrm{1.101001000100001......}$ is the decimal expansion is non termination and non recurring. $\mathrm{71.101001000100001......}$ is a irrational number.