plzz prove that root 6 is irrational.
i have to show the whole prove not just say that 6 is not a perfect square so root 6 is irrational. i have to prove it wholly.
thanks in advance
Assume that is rational.
Then , where are integers, and is in simplest form (since every rational number can be reduced to simplest form).
Since is even, that means is even. So write it as . Then you have
Remembering that is an integer, so is . Also, since 2 is a factor, is even, and so is even. Write it as .
But we said that was already in simplest form.
So we have a contradiction.
This means that can not possibly be rational.
Therefore is irrational.