√5 is Irrennational prove that
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Let root 5 be rational number
Where HCF(p,q) = 1
Therefore , root 5 = p/q
root 5q = p
(root 5)^2 =p^2
5q^2 = p^2
5 is a factor of p^2 (5/p)
5 is a factor of p (5/p)
5/p
P= 5k
(P)^2 = (5k)^2
5q^2 = 25k^2
q^2 = 25k^2 / 5
Therefore , q^2 = 5k^2
5 is a factor of q^2
5 is a factor of q
HCF(p,q) = 5
Our Assumption is contradiction
root5 is irrational number
Where HCF(p,q) = 1
Therefore , root 5 = p/q
root 5q = p
(root 5)^2 =p^2
5q^2 = p^2
5 is a factor of p^2 (5/p)
5 is a factor of p (5/p)
5/p
P= 5k
(P)^2 = (5k)^2
5q^2 = 25k^2
q^2 = 25k^2 / 5
Therefore , q^2 = 5k^2
5 is a factor of q^2
5 is a factor of q
HCF(p,q) = 5
Our Assumption is contradiction
root5 is irrational number
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