Almost anything will work, but why not take the simple example x = y = 1? If square roots behaved as this formula asserts then we would have √2 = √1 + √1 = 1 + 1 = 2, which is clearly absurd.

CBSE 12th Maths Linear Programming Formulas: Check here for all the important formulas of mathematics in Chapter 12 Linear Programming of Class 12, along with major definitions, theorems and examples.