Question

Which of the following is an irrational number?

(a) $\sqrt{23}$

(b) $\sqrt{225}$

(c) 0.3799

(d) $7.\overline{478}$

Answer 1

Since, $\sqrt{225}$ = 15, which is an integer,

0.3799 is a number with terminating decimal expansion, and

$7.\overline{478}$ is a number with non-terminating recurring decimal expansion

Also, 23 is a prime number.

So, $\sqrt{23}$ is an irrational number. $\left[\because \sqrt{n}\mathrm{is}\mathrm{always}\mathrm{an}\mathrm{irrational}\mathrm{number},\mathrm{if}n\mathrm{is}\mathrm{a}\mathrm{prime}\mathrm{number}.\right]$

Hence, the correct option is (a).