This week in math we learned how to convert entire radicals into mixed radicals.
First, find two factors of your radicand, one being a perfect square. Then you will have two radicals, one giving you a whole number, and the other not. This will give you your mixed radical.
Example: In this case you need to find a factor of 75 that is also a perfect square. 25 x 3 is equal to 75, and 25 is also a perfect square. Therefore you square root 25 and move the whole number to the outside of the radical. Therefore 5 x the square root of 3 is equal to the square root of 75.
The same thing can be done with radicals which contain any index. Instead of finding a factor of the radicand that is a perfect square, you find a factor that is either a perfect cube, perfect 4th, etc. depending on the index.
Example: To simplify the cube root of 48, you first need to find a factor of 48 that is a perfect cube. 8 x 6 is equal to 48, and 8 is a perfect cube. You then cube root 8, and again move the number to the outside of the radical. So 2 x the cube root of 6 is equal to the cube root of 48.
