Question

Which of the following is a rational number?

$\left(a\right)\sqrt{2}$

$\left(b\right)\sqrt{23}$

$\left(c\right)\sqrt{225}$

$\left(d\right)\mathrm{0.1010010001....}$

Answer 1

$\left(a\right)\sqrt{2}$

$\sqrt{2}=\mathrm{1.4142135.....}$

It is clearly neither terminating and non-recurring decimal number.

So $\sqrt{2}$ is not a rational number.

$\left(b\right)\sqrt{23}$

$\sqrt{23}=\mathrm{4.79583......}$

It is clearly neither terminating and non-recurring decimal number.

So $\sqrt{23}$ is not a rational number.

$\left(c\right)\sqrt{225}$

$\sqrt{225}=15=\frac{15}{1}$

It is a rational number.

$\left(d\right)\mathrm{0.1010010001....}$

It is clearly neither terminating and non-recurring decimal number. It is not a rational number.

Hence, Option $c$ is correct.