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

1. 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?

2. 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.

3. 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 !!!

4. Re: Show that srt(2)+srt(3)-srt(5+2srt(6)) is rational/irrational

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".

5. 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: