First step: Find out the prime numbers that make up the radical, for example, 120 would be 2x2x2x5x3

Second step: If there is 2 of the same number that repeats just put that number in the front of the resulting radical

Third: Just multiply the remaining radicals together and put the number in front of it.

Now you have

\( 2 \sqrt{30} \)

Example Simplify √252

Step 1: Find the prime factorization of the number inside a radical. 252 = 2 x 2 x 3 x 3 x 7

Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind. √252 = √2 x 2 x 3 x 3 x 7

Step 3: Move each group of numbers or variables from inside the radical to outside the radical. In this case, the pair of 2’s and 3’s moved outside the radical. 2 x 3√7

Step 4: Simplify the expressions both inside and outside the radical by multiplying. 6√7

3^144 what would i do in a case like that ( ^=radical)

well you know that the root of 144 is 12 right?

Just multiply 3 by 12 and you have your answer, 36!