Q. 83.7( 65 Votes )

State whether following numbers are rational or irrational.

(i)

(ii)

Answer :

(i)



We have,



We know √144 = 12 and √100 = 10


So,



= 1.2


Every terminating decimal is a rational number, so 1.2 is a rational number.


(ii)






Now √2,


Consider,



Where p and q are the integers having no common factor and q≠0.



So p2 is an even integer.


p is an even integer.


Let p = 2m


So p2 = 4m2


2q2 = 4m2


q2 = 2m2


q2 is an even integer.


So, q is an even integer.


Since both p and q have common factor 2 and are even. This contradicts the assumption that p and q have no common factor.


Hence √2 is irrational number.


Since, the product of a rational and an irrational is an irrational number.


Therefore, is an irrational.


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