During the first week of school, I learned about entire and mixed radicals, and how I can convert entire radicals to mixed, and vice-versa. I also learned about how I can use perfect square/cube factors of some radicals and factor trees to help me in the conversion.
Firstly, I can quite easily recognize the difference between an entire radical and a mixed radical.
As shown above, entire radicals won’t have any coefficient (number outside the radical sign), while mixed radicals do. Also, if comparing an entire and a mixed radical with the same answer (square root of 18 and 3 root 2), the mixed radical will always be smaller than the original, entire radical.
In terms of converting an entire radical to a mixed radical, I learned that I should determine the two factors of the radical first. One of the factors should be the greatest perfect square or cube factor. Then, all I have to do after is find the square or cube root of the perfect square/cube, and finally combine the two terms so the number I was dealing with is now the coefficient of the new radical.
For converting a mixed radical to an entire radical, it is basically doing the exact opposite steps of what I did with converting entire radicals to mixed form. First, I just have to multiply the coefficient by itself (squaring is the opposite of square root), then I multiply the new coefficient with the radical to get an entire radical. 
Converting an entire radical to a mixed radical and a mixed to an entire radical is also quite easy, as long as I’m dealing with smaller numbers. But if I ever need somewhere to start, I can use a perfect square/cube table to help find whether a radical is a perfect square or cube, or to help find a greatest perfect square/cube factor.
For even larger radicals, using a factor tree instead will help me a lot more in finding the greatest perfect square/cube factor in a radical, than using a square or cube table. This is due to the radical likely having more perfect factors, so I would have to go through a long list of perfect squares/cubes in order to find the greatest of them all.
If I rewrote this as 2 cube root 32, it would still give me the same answer as 4 cube root 4 (6.34…). However, I am not using the greatest perfect cube factor of 256, and in most cases the answer to a question is the greatest perfect factor of a radical, so 64 (4^3) would be the perfect cube factor and not 8 (2^3).