prove that is irrational
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to prove :-√5 is irrational
solution:-
let √5 be rational
√5=p/q
(√5)^2=p^2/q^2
5=p^2/q^2
5q^2=p^2. (1) equation
q^2=p^2/5
here p^2 is divided by 5
let p=5m
put in equation( 1)
5q^2=(5m)^2
5q^2=25m^2
q^2=5m^2
q^2/5=m^2
here q^2 is divided by 5
hence it can not be possible that both p^2 and q^2 divided by 5
hence proved
that √5 is a irrational number
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