Week 2 in math 10

Week 2 in math 10

Something that I learned this week is how to convert entire radicals into mixed radicals and vice-versa. In the beginning, I was a bit confused but after doing the homework and asking my classmates for help I began to understand.

This is the process I use to convert the entire radical. First, I would use prime factorization on the radicand, then from there I would look at the index, for example,  in $\sqrt[4]{48}$ the index is 4, meaning that after finding the prime factorization of 48 you would look for the same prime numbers and place them in groups of 4.(Depending on the index given that indicates how many prime numbers are placed in one group.) The prime numbers that are in a group are placed on the outside of the radical which becomes the coefficient, and all the remainders that were not grouped are either multiplied together or left alone. If the remainders are multiple different groups of prime numbers you multiply them, but if there is only one group of the same prime number there’s nothing to multiply it by so you leave it as it is. The remainders stay on the inside of the radical.

Ex.