Number Systems — Question 9

(i) $\sqrt{23}$ is a prime number. It is irrational because $\sqrt{23}$ does not have a complete root.

(ii) $\sqrt{225}$ is not a prime number. 15 is root of $\sqrt{225}$ so it is rational.

(iii) 0.3796 is terminating decimal expansion. Hence, it is rational.

(iv) 7.478478... = $7.\overline{478}$, it is non-terminating but repeating decimal expansion. Hence, it is rational.

(v) 1.101001000100001... is non-terminating and non-repeating decimal expansion. Hence, it is irrational.