Download Simplifying Radical Expressions

Unit 1:
Radical Expressions
I can Simplify a perfect square radical
expression
Learning Target #1
What does ______ mean?
• Simplify
• Perfect Square
• Radical Expression
What is the Square Root of each Value?
•0
• 36
•1
• 49
•4
• 64
•9
• 81
• 16
• 100
• 25
• 121
Simplify Each Radical Expression
•
0
•
36
•
1
•
49
•
4
•
64
•
9
•
81
•
16
•
100
•
25
•
121
Bell Work: Simplify the Single Radical Expression
1. 24
2. 50
Simplifying Single Radical Expressions: Methods
• Prime Factorization
• Tree Method
• Pyramid
• Perfect Square Factor
Prime Factorization (Tree Method or Pyramid)
1.
Start with your number at the top of the Tree
2.
Break it down into two numbers that multiply to get that number (2 Factors)
3.
If either number is PRIME, that side of the tree is finished, continue breaking down what remains.
4.
Continue finding factors of each new number until you are left with only PRIME numbers.
5.
Once all numbers are PRIME, find ALL pairs of PRIME numbers that are the same.
6.
Each pair of numbers represent a number that will be MULTIPLIED out in front of the radical/ square
root.
7.
If there are multiple pairs, pull out each pair and multiply them together.
8.
Leave all numbers that don’t have a pair under the radical and multiply them together.
9.
The final answer will be ONE number multiplied by the square root with ONE number underneath.
Prime Factorization Examples
108
32
147
Perfect Square Factor Method
1. Find the LARGEST/ BIGGEST perfect square (4, 9, 16, 25, etc.) that is a factor of
your original number.
2. Break down the radical into the perfect square factor multiplied by the factor that
matches the perfect square.
3. Take the square root of the perfect square and put that number out in front of the
radical/ square root.
4. WARNING!!! If you do not find the BIGGEST perfect square factor, you will have
to factor more than once!
Perfect Square Factor Method: Examples
108
32
147
Order of Operations
1. Parentheses
2. Exponents
3. Multiplication/ Division
4. Addition/ Subtraction
Use Order of Operations of Simplify
4 + 12
4 + 12