Classify the following numbers as rational or irrational:(i) √23(ii)

1.	Classify the following numbers as rational or irrational:(i) √23(ii) √225(iii) 0.3796(iv) 7.478478…(v) 1.101001000100001…
Answer» (i) √23 Here, 23 is not a perfect square number, hence, √23 is an irrational number. (ii) √225 Here 225 is a perfect square of 15, hence √225 is a rational number. (iii) 0.3796 can be written in \(\frac { p }{ q }\) form, where q ≠ 0 i.e \(\frac { 3796 }{ 10000 }\) Hence, it is a rational number. (iv) 7.478478 i.e. \(7.\bar { 478 } \) Here, pair of digits (478) are repeating as it is non-terminating but recurring. (v) 1.101001000100001…. is an irrational number is its decimal expansion is non-terminating and non-recurring.

Classify the following numbers as rational or irrational:(i) √23(ii) √225(iii) 0.3796(iv) 7.478478…(v) 1.101001000100001…

Answer»

(i) √23

Here, 23 is not a perfect square number,

hence, √23 is an irrational number.

(ii) √225

Here 225 is a perfect square of 15,

hence √225 is a rational number.

(iii) 0.3796 can be written in \(\frac { p }{ q }\) form,

where q ≠ 0 i.e \(\frac { 3796 }{ 10000 }\)

Hence, it is a rational number.

(iv) 7.478478 i.e. \(7.\bar { 478 } \)

Here, pair of digits (478) are repeating as it is non-terminating but recurring.

(v) 1.101001000100001…. is an irrational number is its decimal expansion is non-terminating and non-recurring.