Show that 3-underroot2 is irrational

Step-by-step explanation:

Hello,

Basically, we need to prove that is irrational

Let s assume that is rational

it means that we can find p and q (q different from 0) two integers with no common factors other than 1

so that

And then we can write that

So is even so it means that p is even

so is divisible by 2*2=4

as   it means that is even, meaning q is even

wait, p and q are then even !? but by definition they have no common factors. This is not possible.

so our assumption that is rational is false

So it means that this is irrational

and then is irrational too

Hope this helps

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