Radicals

Radicals

1. Simplifying Radicals

   • Step 1: Find the prime factorization of the number inside the radical. 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. 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. Step 4: Simplify the expressions both inside and outside the radical by multiplying.
   • To simplify radicals, rather than looking for perfect squares or perfect cubes within a number or a variable the way it is shown in most books, I choose to do the problems a different way, and here is how.
   • MAKE A LIST OF THEM. 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
   • The radical cannot be a fraction can be taken care of by first simplifying the fraction if possible.

2. Add and Subtract Radicals

   • Step 1: Simplify each radical. Step 2: Add or subtract the radicals. Remember that we can only combine like radicals.
   • Two radicals that have the same index and the same radicals (the expression inside the radical) are called like radicals.
   • Like radicals can be added (or subtracted) in the same way as like terms. We apply the distributive property and then combine the coefficients

3. Multiplying Radicals

   • 1)Multiply the coefficients and the radicals separately (do not cross the streams!!!) 2)Simplify the radicand at the end
   • Instead, the goal will be to make the radicand as small as possible
   • It is possible that no perfect squares will divide evenly into the radicand. If this is the case, then it is possible that the expression cannot be simplified