Find which numbers of the following numbers are rational and which numbers are irrational.

i. √23

ii. √225

iii. 0.3797

iv. 7.4784478….

v. 1.101001000100001…..

Rational numbers are the numbers which can be expressed in p/q form or simply which have a terminating or repeating decimal expansion.

On the other hand, irrational numbers are the numbers with non repeating and non terminating decimal expansion.

i. √23

Since 23 can’t be expressed as any number’s perfect square.

⇒ √23 is irrational.

ii. √225

Since 15² = 225

⇒ √225 = √15² = 15

√225 is rational.

iii. 0.3797

Since 0.3797 is terminating and non-repeating and can be expressed in the form of

⇒ 0.3797 is rational

iv. 7.4784478….

Since 7.4784478… is non-terminating and cannot be expressed in the form of

⇒ 7.4784478…. is irrational

v. 1.101001000100001…..

Since 1.101001000100001….. is non-terminating and cannot be expressed in the form of

⇒ 1.101001000100001… is irrational