I'm on the bench at work, so I spend my days following along with examples in Python books.  Whenever there is a choice to use  x**0.5 or math.sqrt(x) the books opt for the square root option instead of the equivalent representation as a fractional power.  Is the implementation of math.sqrt() more efficient than x**0.5?  Is there a numerical shortcut to the value of sqrt(x) that will make the sqrt symbol more efficient than the power equivalent (x^0.5) in every programming language?