How to simplify radicals
Step 1: Find the prime factorization of the number inside the radical.
- Start by dividing the number by the first prime number 2 and continue till you get a remainder.
- Then move up to the next prime 3, 5, 7, etc... until the only numbers left are prime.
- Finally factor any variables inside the radical.
Step 2: Find the Index.
- The index tells you how many of a set you need to put together to be able to move that number or variable from inside the radical to outside the radical.
- The index of a square root is 2 the index of a cube root is 3 etc...
Step 3: Move each group of numbers/variables from inside the radical to outside the radical.
- If there are not enough numbers/variables to make a set for the index then leave those inside the radical.
- In 18 there are two sets of 3 so a single 3 can be taken out of the radical, if there were four 3's two of them would be taken out of the radical.
- If dealing with a higher index, on the radical then you need to match the sets with the index
Step 4: Simplify the expressions both inside and outside the radical by multiplying.
Examples
