What is the conjugate of x-square root of 2

The conjugate of a binomial, is pretty much just the same thing, but with a different sign in between, so,

pelican + canary conjugate = > pelican - canary

a + b conjugate = > a - b

-a - b conjugate = > - a + b

and so on, therefore

x - √2 conjugate = > x + √2