Prove that root5 is irrational in contradiction method
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Let root 5 is rational number
a÷b =√5 , a & b are co-prime
a = b√5
squaring both sides
a^2 = (b√5)^2
a^2 = 5b^2. ----------- (1)
a^2 is divides by 5 than a is also divides by 5
Again , take
a = 5c
a^ 2 = (5c)^2
a^2 = 25c^2. ------------(2)
from 1 & 2 ,we get
5b^2 = 25c^2
b^2 = 5c^2
b^2 is divides by 5 than b is also divides by 5
than 5 is common factor of a & b
it is contradiction, because a & b are co- prime
so, √5 is a irrational number
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