# Proof irrational

• May 16th 2010, 08:06 PM
statman101
Proof irrational
Can anyone give a complete proof step by step that the:

sqrt(41)+5=irrational
given that the sqrt(41) is irrational..

Show that it is irrational by the fact that the
sqrt(41) is irrational.
• May 16th 2010, 08:09 PM
roninpro

What happens if $\sqrt{41}+5$ is irrational?
• May 16th 2010, 08:13 PM
statman101
I have the sqrt(41)+5=p/q
but how does it help knowing the sqrt(41)=irrat.
• May 16th 2010, 08:14 PM
roninpro
What if you subtract 5 from both sides?

$\sqrt{41}=\frac{p}{q}-5$

Anything wrong with this?
• May 16th 2010, 08:20 PM
statman101
still cant see it
• May 16th 2010, 08:24 PM
roninpro
We have a rational $\frac{p}{q}$ subtract another rational $5$. What kind of number results?
• May 16th 2010, 08:44 PM
statman101
Rat - rat = rat
I tried the prob before I submited it..
I appreciate u trying to me to get to think but
I posted it to get a complete proof..
You have it right there. First, you are given that $\sqrt{41}$ is irrational. Then, you said that $\sqrt{41}=\frac{p}{q}-5$ is rational, since a rational subtract a rational is rational. Hence, $\sqrt{41}$ is rational and irrational.
$\sqrt{41}=\frac{p}{q}-5=\frac{p-5q}{q}=\frac{p'}{q} \in \mathbb{Q}$.