Hello! I have a friend who needs some help getting this problem. I'm afriad I am a little unavailable to help currently, so I had to come to you guys, since I know you are the best! Any help or info that can be provided is greatly appreciated. I sincerely thank you all for all that you do and all the time you deticate to helping us all. Have a nice day and thank you in advance!

Guest Mar 21, 2018

#1**+1 **

Alright, here we go:

In n/m, both are relatively prime and cannot simplify the fraction.

To prove that √3 is irrational from n^2 = 3m^2

From n^2 = 3m^2, we can say that n is a multiple of 3, since there is a 3 on the right side of the equation.

We can set n equal to 3k

So n^2 = 9k^2 = 3m^2

3k^3 = m^2

So this means that m is also a multiple of 3.

In the beginning we stated that they are relatively prime and cannot simplify, but if both are n and m are multiples of 3, how is this possible?

This leads to a contradiction.

supermanaccz
Mar 21, 2018