Julian
]]>Apologies about the confusion with posting in two forums.
Jack
]]>Bob
]]>Bob
]]>He posted again in help and I replied there.
If p^2 is divisible by 5, how do you know that p is also divisible by 5 ?
(I know it is, but I want a justification please. Otherwise every root is irrational.)
Bob
]]>So:
sqrt(5)=p/q
Then we square both sides:
5=p^2/q^2
5*q^2=p^2
So this means that p must be divisible by 5, and we can write p=5*r and our equation becomes:
5*q^2=25*r^2
q^2=5*r^2,
But this would mean that q is also divisible by 5, and we said that p and q have a gcd of 1! This is a contradiction, so our initial assumption that sqrt(5) is rational is false!