Exponents and Variables: Radicals

If  is a positive integer and is a real number, then:

-  A square root of is a number whose square is: ( is a square root of )
-  To add and subtract radicals, we need to have the same values under the radical. For example: ,
 

Examples:
Example 1.  Find the square root of .
Solution: First, factor the number: , Then: ,
Now use radical rule: . Then:

Example 2.  Evaluate.
Solution: Find the values of and . Then:

Example 3.  Solve. .
Solution: Since we have the same values under the radical, we can add these two radicals:

Example 4.  Evaluate.
Solution: Use this radical rule:
The square root of is . Then: