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