Radicals

Radicals are mainly numbers under a square root sign. There are some basic rules to multiplying and simplifying radicals.

 

  1. - Numbers outside the square root sign multiply normally and seperately from the     numbers on the inside.
  2. - If the numbers under the square root signs are the same, then the square root sign is gone. (i.e. \sqrt(3) X \sqrt(3) = 3)
  3. - Radicals can only be added or subtracted if the numbers under the square root sign are the same.

 

Example 1:

 

 

Radical Example 1

 

In this example, the 4 is multiplied by the 2. Since the numbers under the square root signs are the same, they cancel out. Therefore, what is left is 8*5 which is 40.

 

Example 2:

 

 

Radical Example 2

 

This problem must be apporached using binomial multiplication. This is when the first term is multiplied by the 2 terms in the second bracket and the second term is multiplied by the 2 terms in the second bracket. Since this is a difference of squares, two of the terms end up being cancelled out. Using the rules shown in Example 1 and basic multiplication, the answer ends up to be 90.

 

 

Example 3:


Radical Example 3

 

This example has a bit of a trick in it. First, it is usually best to have no radicals in the bottom of a fraction, this is called rationalizing the denominator. To do this, use the conjugate which is basically the same expression as the denominator, however with a different sign in the middle (+ or -). After the conjugate is used, it is similar to other examples.

 

If you have any questions, leave them in the comments.