Separate the rationals and irrationals from among the following numbers :

(i) -8

(ii) $\sqrt{25}$

(iii) $\dfrac{-3}{5}$

(iv) $\sqrt{8}$

(v) 0

(vi) π

(vii) $\sqrt[3]{5}$

(viii) $2.\overline{4}$

(ix) $-\sqrt{3}$

(i) -8 can be expressed in the form of $\dfrac{p}{q}$, where p and q are integers and q ≠ 0.

Hence, -8 is a rational number.

(ii) $\sqrt{25} = 5 = \dfrac{5}{1}$

Thus, $\sqrt{25}$ can be expressed in the form of $\dfrac{p}{q}$, where p and q are integers and q ≠ 0.

Hence, $\sqrt{25}$ is a rational number.

(iii) $\dfrac{-3}{5}$ can be expressed in the form of $\dfrac{p}{q}$, where p and q are integers and q ≠ 0.

Hence, $\dfrac{-3}{5}$ is a rational number.

(iv) $\sqrt{8}$ is square root of non-perfect square i.e. 8.

Hence, $\sqrt{8}$ is an irrational number.

(v) 0 can be expressed in the form of $\dfrac{p}{q}$, where p and q are integers and q ≠ 0.

Hence, 0 is a rational number.

(vi) π is a non-terminating and non-repeating decimal.

Hence, π is an irrational number.

(vii) $\sqrt[3]{5}$ is cube root of non-perfect cube i.e. 5.

Hence, $\sqrt[3]{5}$ is an irrational number.

(viii) $2.\overline{4}$ is a repeating decimal.

Hence, $2.\overline{4}$ is a rational number.

(ix) $-\sqrt{3}$ is square root of non-perfect square i.e. 3.

Hence, $-\sqrt{3}$ is an irrational number.