Question:
Which of the following is an irrational number?
(a) $\sqrt{23}$
(b) $\sqrt{225}$
(c) $0.3799$
(d) $7 . \overline{478}$
Solution:
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. $\quad[\because \sqrt{n}$ is always an irrational number, if $n$ is a prime number. $]$
Hence, the correct option is (a).