Perfect square root of a quadratic

Is it possible to find analytically the function that forms the perfect square root of a quadratic in all cases?

For example with the quadratic x^2 + 10x + 25 you can find by factoring the perfect root x + 5. But how do you find the square root when a quadratic isn't expressed in the form of the completed square?

With the quadratic x^2 + 10x + 20 it seems the simplest form you can get the root into is sqrt((x+5)^2 -5)).

Is that the best that can be done? Is there some other way to express this root?