An nth root algorithm is a way to figure out what number you have to multiply itself a certain number of times to get another number. For example, if you wanted to find out what number you would need to multiply itself 2 times to get 8, you can use an nth root algorithm. Think of it like a math trick.
The algorithm works by taking the number we want to find the root for (in this case 8) and then dividing it by the number of times the root should be multiplied (in this case 2). This number is then multiplied by itself the same number of times (in this case 2). When you do this calculation, the answer you get is the number that, when multiplied the same number of times you used in the equation (in this case 2), returns the number we were looking for (8).
So In this example, if we divide 8 by 2, we get 4. So when we multiply 4 by itself 2 times, we get 8. So the answer we got (4), when multiplied by itself 2 times, equals 8.