Have fun in the forum, Jackme12!

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!