**Question:**

Classify the following numbers as rational or irrational:

(i) $\frac{22}{7}$

(ii) $3.1416$

(iii) $\pi$

(iv) $3 . \overline{142857}$

(v) $5.636363 \ldots$

(vi) $2.040040004 \ldots$

(vii) $1.535335333 \ldots$

(viii) $3.121221222 \ldots$

(ix) $\sqrt{21}$

(x) $\sqrt[3]{3}$

**Solution:**

(i) $\frac{22}{7}$ is a rational number because it is of the form of $\frac{p}{q}, q \neq 0$.

(ii) 3.1416 is a rational number because it is a terminating decimal.

(iii) $\pi$ is an irrational number because it is a non-repeating and non-terminating decimal.

(iv) $3.142857$ is a rational number because it is a repeating decimal.

(v) 5.636363... is a rational number because it is a non-terminating, repeating decimal.

(vi) 2.040040004... is an irrational number because it is a non-terminating and non-repeating decimal.

(vii) 1.535335333... is an irrational number because it is a non-terminating and non-repeating decimal.

(viii) 3.121221222... is an irrational number because it is a non-terminating and non-repeating decimal.

(ix) $\sqrt{21}=\sqrt{3} \times \sqrt{7}$ is an irrational number because $\sqrt{3}$ and $\sqrt{7}$ are irrational and prime numbers.

(x) $\sqrt[3]{3}$ is an irrational number because 3 is a prime number. So, $\sqrt{3}$ is an irrational number.