Q. 13.7( 3 Votes )

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…..

Answer :

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


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