Ok so I am to prove: If x is irrational, then [tex]\sqrt{x}[/tex] is irrational. So I started by trying to prove the contrapositive: If [tex]\sqrt{x}[/tex] is rational, then x is rational.(adsbygoogle = window.adsbygoogle || []).push({});

So then [tex]\sqrt{x} = \frac{m}{n}[/tex] For integers m and n, n[tex]\neq[/tex]0

Then square both sides. [tex]x = \frac{m^2}{n^2}[/tex]

This is clearly rational because m^2 and n^2 are integers.

Now, is this a satisfactory proof? I am sure it is, it just seems as though it was too easy. Did my teacher ask it because it shows how proving the contrapositive can sometimes make life easy? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof: x is irrational => sqrt(x) is irrational

**Physics Forums | Science Articles, Homework Help, Discussion**