Classify the following numbers as rational or irrational.

i.

ii.

iii. 30.232342345…

iv. 7.484848…

v. 11.2132435465

vi. 0.3030030003.....

(i) On prime factorization 27 = 3³

√(3³) = 3√3

√3 is an irrational number and so √27 is an irrational number

(ii) On prime factorization 441 = 7² × 3²

√(7² × 3²) = 21

Since 441 is a perfect square so square root of it is a rational number

(iii) The decimal is not terminating in case of this number.

So it can never be expressed in the form of fraction i.e. numerator by denominator.

So the number is an irrational number.

(iv) The decimal is not terminating in case of this number.

So it can never be expressed in the form of fraction i.e. numerator by denominator.

So the number is an irrational number.

(v) The decimal is a terminating decimal number.

So it can be expressed in the form of fraction i.e. numerator by denominator.

So the number is an rational number.

So it can never be expressed in the form of fraction i.e. numerator by denominator.

So the number is an irrational number.

(vi) The decimal is not terminating in case of this number.

So it can never be expressed in the form of fraction i.e. numerator by denominator.

So the number is an irrational number.