Is the Sum of Square Roots of 2 and 3 Irrational? A Proof by Contradiction

[MathematicalPhysics]

Yeh just having a problem seeing a way to prove that 6^(1/2) is irrational.

Using this answer and proof by contradiction I need to prove that
2^(1/2) + 3^(1/2)is also irrational, however I sould be able to attempt this if I can get the above right.

Any help much appreciated.

 

[matt grime]

Here's a better proof than contradiction.

let z be the sqrt of any integer, if it is rational write it as a/b, do the usual squaring thing so that

z.b^2= a^2

look at the prime decompostions on both sides. Every prime mus occur with multiplicity two on the rhs, so it does on the lhs, which tells us in the prime decomposition of z every prime occurs twice, that is z is a perfect square. 6 is not a perfect square.

 

[MathematicalPhysics]

Thanks for that, the rest worked out a treat!