Irrational numbers?

Question

If i add 2 irrational numbers together..it is possible to get an answer that is not irrational. But i cannot find an example for it. Can some1 help pls?
(Irrational numbers are those that cant be expressed as fraction...eg square root 2, square root 3, pi,....)

Only addition is allowed....no other signs

Answer 1

The sum of a irrational number with a rational number is always irrational. So, take, for example, a = sqrt(2) and b = 3 - sqrt(2). Then, a and b are irrational, but a + b = 3, which is rational.

Answer 2

It's possible for examle the irrational e
e - e = 0 which is rational while e and -e are irrational. Also something like 1+sqrt(2) + 1-sqrt(2) = 2 so it is possible.

Answer 3

2+sqrt3 =3.7321 is irrational; so is 2-sqrt3, which is 0.2679...
Their sum is ... 4
There are countless examples like that.
However this work only because I add and subtract the same irrational (sqrt3 in this case).
This won't work otherwise. No combination of sqrt 2,3,5 or whatever will come as an integer unless the sqrts are somehow cancelled. (evidently sqrt n^2, or cubic roots of cubes, etc are excluded from my argument)

Edited 2 minutes later: you want addition only so 2-sqrt3 has to be replaced by 2+(-sqrt3) !

Answer 4

I think a simple answer would be the following. (I'm using sqrt to mean "the square root of")
1+sqrt2 is an irrational number, and so is
1-sqrt2.
Adding them together gets you 2, which is rational.

Answer 5

Actually, in Trigonometry, there's a very simple example:
Take a number (marked by x) and put in this equation:

(sin x)^2 + (cos x)^2 = 1

Answer 6

Your teacher has the answers

Answer 7

yes it is possible.let the irrationa nos be n1 and n2
n1=1.01001000100001.........................
n2=0.10110111011110........................
n1+n2=1.11111111111.......................... which is a rational number

Answer 8

no it is not