# Show that srt(2)+srt(3)-srt(5+2srt(6)) is rational/irrational

• Jan 22nd 2014, 07:54 PM
kinhew93
Show that srt(2)+srt(3)-srt(5+2srt(6)) is rational/irrational
srt(2)+srt(3)-srt(5+2srt(6))

Show that this is rational/irrational

Can someone give me an idea of where to start?
• Jan 22nd 2014, 08:15 PM
ibdutt
Re: Show that srt(2)+srt(3)-srt(5+2srt(6)) is rational/irrational
we know that sum / difference of two irrational numbers is irrational unless we are subtracting the same irrational number in which case the result will be 0. That should give you a beginning.
• Jan 23rd 2014, 03:16 AM
MINOANMAN
Re: Show that srt(2)+srt(3)-srt(5+2srt(6)) is rational/irrational
Ibdutt you are missing something?
let r1 be a rational number and r2 another rational then r1+π is irrational and r2-π is also irrational ..but (r1+π)+(r2-π) IS A RATIONAL AND NOT IRRATIONAL number !!!
• Jan 23rd 2014, 03:06 PM
Prove It
Re: Show that srt(2)+srt(3)-srt(5+2srt(6)) is rational/irrational
Quote:

Originally Posted by MINOANMAN
Ibdutt you are missing something?
let r1 be a rational number and r2 another rational then r1+π is irrational and r2-π is also irrational ..but (r1+π)+(r2-π) IS A RATIONAL AND NOT IRRATIONAL number !!!

I'm sure ibdutt meant "subtracting the same irrational number PART".
• Jan 25th 2014, 09:48 AM
johng
Re: Show that srt(2)+srt(3)-srt(5+2srt(6)) is rational/irrational
Hi,
I assume "srt" means square root. I don't know how to give you a hint without answering the question. So the attachment gives a solution:

Attachment 30076