The principal square root of 729 is 27. It is called the "principal square root" because it is a non-negative number. The number 729 actually has two square roots, 27 and negative 27, but positive 27 is what is generally referenced to as the "square root".
In this particular example, the square root of 729 is the number that, when multiplied by itself, is equal to 729. If you multiply 27 by 27, you get 729. Also, if you multiply negative 27 by negative 27, you get 729, since multiplying two negative numbers equals a positive number. This is why 729, and any other positive number, will always have two square roots, one positive square root and one negative square root.
In math, the root function is the inverse of the exponential function, so the inverse of taking a square root is squaring a number. Using the above example, 27 squared is equal to 729.