If root ab be an irrational number then prove that root a+ root b is irrational

Given: √ab is an irrational number.

To Prove :   √a +√b  is irrational.

Now, suppose, 

  √a +√b be rational.

As, √a +√b  is rational.

⇒ x and y will be rational .

∴ R.H.S. of equation (i) is rational

whereas L.H.S. of (i) is given to be irrational

which contradicts our supposition

Hence √a +√b  is not rational 

∴ √a +√b  is irrational