Thread: Prove by contradiction

Prove by contradiction that if r is irrational, then r^(1/2) is irrational

Originally Posted by hebby

Prove by contradiction that if r is irrational, then r^(1/2) is irrational

Where are you stuck? This is straight fwd
Hint: If x is rational, what can you say about x^2?

well then r^2 is rational as well, eg)4^2 is rational..then what?...thats it?

Originally Posted by hebby

well then r^2 is rational as well, eg)4^2 is rational..then what?...thats it?

yep !!

so if sqrt(r) is rational => r is rational (Contradiction !!)

Thanks, but we r going the other way around....ie if r is rational then sqrt r is rational.

Originally Posted by hebby

Thanks, but we r going the other way around....ie if r is rational then sqrt r is rational.

Absolutely not.
We are saying "if sqrt r is rational then r is rational"
Plz note the difference carefully

but the questions says if r is irrational then the sqrt r is irrational so we have to work this way right?

Originally Posted by hebby

but the questions says if r is irrational then the sqrt r is irrational so we have to work this way right?

dnt confuse yourself. both the statements are equivalent. one implies the other and vice-versa.

if sqrt r is rational then r is rational (we proved it)
but r is irrational (as per the question)
that mean sqrt r can't be rational because otherwise r will be rational (a contradiction)
hence sqrt r must be irrational !!