Prove that under root 7 is irrational number
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assume that √7 be rational.
then it must in the form of p / q [q ≠ 0] [p and q are co-prime]
√7 = p / q
=> √7 x q = p
squaring on both sides
=> 7q2= p2 ------> (1)
p2 is divisible by 7
p is divisible by 7
p = 7c [c is a positive integer] [squaring on both sides ]
p2 = 49 c2 --------- > (2)
subsitute p2 in equ (1) we get
7q2 = 49 c2
q2 = 7c2
=> q is divisble by 7
thus q and p have a common factor 7.
there is a contradiction
as our assumsion p & q are co prime but it has a common factor.
so that √7 is an irrational.
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