The square root of a number, let's say X, where another number, let's say Y, has the following property. YxY=X
Not all numbers have integer square roots. In fact, most do not. There is also a bit of algebra associated with square roots. But that is the jist of it.
I'm not familiar with three types of percentages. Maybe you mean decimal, fraction, and percentage representations. Is this maybe what you're talking about?
The first number must be between 1 and 10. From there, if the power that 10 is raised to is positive, move the decimal place to the left that many times. If it is negative, most the decimal place that many times to the right.