- #1

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## Homework Statement

Prove that [itex] \sqrt{6} [/itex] is irrational.

## The Attempt at a Solution

Would I just do a proof by contradiction and assume that [itex] \sqrt{6} [/itex] is rational and then get that [itex] 6q^2=p^2 [/itex] which would imply that p is even so I put in p=2r

and then multiply it out. then this would imply that q is also even and this is a contradiction because they would have factors in common. I know I skipped some of the steps. Could I also make an argument that [itex] \sqrt{6} [/itex] is [itex] \sqrt{3}\sqrt{2} [/itex] and then say that an irrational times an irrational is an irrational as long as its not the same irrational.