Advanced Algebra Notes Section 4.5: Simplifying Radicals (A) A number r is a _____________ of a number x if. The number r is a factor that is used twice (the same number twice) to get the number x. EX:, r = 7 because A positive number x has two square roots EX: The symbol is called a _____________, the number inside the radical sign is called the _____________, and the expression is called a _____________. A square root is ___________ when the following is true; 1. ____________________________________________________________. 2. _____________________________________________________________. If you do have a radical left in a denominator you can get rid of it by ________________ ______________. square root radical sign radicandsquare root simplified No perfect square factors other than 1 inside the radical sign No radicals left in the denominator, or fractions inside a radical symbol rationalizing the denominator

When you rationalize a denominator you are multiplying the numerator and the denominator by the same radical (form of 1). The radical must make the denominator a perfect square so the radical will drop out of the denominator. You can use the following properties when simplifying expressions containing square roots. Product Property: Quotient Property: Examples: Simplify the following expressions. 1) 2) 3)