Q.9. Classify the following numbers as rational or irrational:

(i) $\sqrt{23}$ (ii) $\sqrt{225}$ (iii) 0.3796

(iv) 7.478478… (v) 1.101001000100001…

Solution:

(i) $\sqrt{23}$ = 4.79583152331...

Square roots of all the numbers, except perfect squares are irrational. Hence it is an irrational number.

(ii)

$=\frac{\text{15}}{\text{1}}$

All integers (like 15) can be represented in the $\frac{\mathrm{p}}{\mathrm{q}}$ form, hence it is rational number.

(iii) 0.3796

Since the number is terminating therefore, it is a rational number.

(iv) 7.478478… = 7.$\stackrel{‾}{478}$

Since this number is non-terminating recurring, it is a rational number.

(v) 1.101001000100001…

Since the number is non-terminating non-repeating, it is an irrational number.