As you may already know, a prime number is one that has exactly two factors, 1 and itself. No number will divide a prime number and create a non decimal answer. It turns out too, that when you break down a number into its factors, the factors are always prime, whether the number itself is or not. This is especially useful when doing square roots. For example, when you factor the number 36, you get 2*2*3*3. This also means the root of 36 is root(2*2*3*3). Since the square root of a number times itself is just the number, it is easy to see that for each repeated number under the square root sign, we can pull one out as a whole number. So the square root of 36 is 2*3, or 6.
The same thing can be done for prime numbers, but you won't get any actual factors, and it would be silly to write 1 as a factor; it's kind of a given. Nonetheless, this same thing can be done for much larger numbers too. If we wanted to find root(220,000) we would of course need a calculator and the best place to start would be dividing by 2 because it is obvious that 2 will divide it. Anyway, we find that the factors are 2*2*2*2*2*5*5*5*5*11. So root(220,000) equals 2*2*5*5*root(5*11) or 100*root(55).
The same thing can be done for prime numbers, but you won't get any actual factors, and it would be silly to write 1 as a factor; it's kind of a given. Nonetheless, this same thing can be done for much larger numbers too. If we wanted to find root(220,000) we would of course need a calculator and the best place to start would be dividing by 2 because it is obvious that 2 will divide it. Anyway, we find that the factors are 2*2*2*2*2*5*5*5*5*11. So root(220,000) equals 2*2*5*5*root(5*11) or 100*root(55).