How can you use prime factorization to make what are perfect cubes and perfect squares?

When you prime factorize, u will get a series of 2s, 3s, 5s.......... as your prime factors. If you are finding the square root, then group 2 of the same numbers together and take them as 1. Eg: 625: on factorizing u will get 5*5*5*5 since there are 4 5s, group 2 together, and take them as one: 5*5-----, 5*5--------, and take them as 1: 5*5 = 5, 5*5 = 5, and multiply them. 5*5 = 25. Therefore, the square root of 625 is 25. For the cube root, you do the same thing but group 3 numbers together, but they should be the same number, eg: 216: 2*2*2*3*3*3: 2*2*2--------, 3*3*3--------: 2*3: cube root is 2*3: 6.

This way you can determine whether the number is a perfect square, cube..........

Hope it helped!!