Prove that √5 is irrational.

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Sir please read this
Let assume
p/q= √4
p=q*√4
p^2=4* q^2...(i)
Since , p is natural no. So p's square factor is also factor of p
So , 4 is also factor of p
Thus p= 4c....(ii)
Now put this eq in eq(i), we get
q^2=4*c^2
Also here 4 is factor of q
Thus q= 4d
Now ,
p/q=4c/4d
But we assume p and q are prime then
√4 is irrational no
WTF 😢

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