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.

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

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