1. Simplifying Radicals

2. A radical is any algebraic statement with this symbol:
What is a Radical?
A radical is any algebraic statement with this symbol: 2
This is called the RADICAL
The number under here is called the RADICAND

3. Before you can simplify…
We need to know what a perfect square is!
A perfect square is any number created by squaring another number.
Ex: =9 9 is the perfect square!
Ex: = is the perfect square!

4. What are all the perfect squares up to 100?
1 2 =1 2 2 =4 3 2 =9 4 2 = = = = = = =100
These are the perfect squares

5. First 10 Perfect Squares
It would be a good idea to write down and memorize the first 10 perfect squares!
Here they are again:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100

6. Now that we know our P.S.’s we can begin
Find the biggest Perfect Square that goes into the RADICAND (the number under the radical) evenly.
Example: = 100∙2 (always put the P.S. first)
Separate the radical into two new radicals.
Example: = 100∙2 = ∙ 2
Take the square root of the P.S. radical and “free” it. Leaving the second radical alone.
Example: 200 = 100∙2 = ∙ 2 =10∙ 2

7. Practice
Simplify the following radicals if possible. 75 32 27 13 8

8. Getting Rid of a Radical in the Denominator

9. First things first… How do you undo square root?
What do you get when you square the square root of 6?
6 2 =
Trick question…What is ?
We call this a “crafty” form of 1.

10. We don’t like having radicals in our denominators!
To get rid of a radical in the denominator you must:
Multiply the entire fraction by a “crafty” form of 1. (remember when multiplying fractions multiply across the top, multiply across the bottom)
Example: ∙ = 4∙ ∙ 2
Simplify the denominator.
Example: ∙ = 4∙ ∙ 2 = 4∙ 2 2
Simplify the numerator and denominator if possible.
Example: ∙ = 4∙ ∙ 2 = 4∙ = 2∙ =2 2

11. Practice
Simplify the following fractions:
5 3
10 2
3 6
11 5
8 3