1. Simplifying Non-Perfect Squares

2. Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1):
The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions based on contextual situations. 4 3 2 1
In addition to level 3.0 and above and beyond what was taught in class,  the student may:
·  Make connection with other concepts in math
·  Make connection with other content areas.
The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions on contextual situations.
- justify the  sums and products of rational and irrational numbers
-interpret expressions within the context of a problem
The student will be able to use properties of rational and irrational numbers to write and simplify  expressions based on contextual situations.
-identify parts of an expression  as related to the context and to each part
With help from the
teacher, the student has
partial success with real number expressions.
Even with help, the student has no success with real number expressions.

3. Know Perfect Squares 12 = 1 22 = 4 32 = 9 212 = 441 222 = 484 42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400
212 = 441
222 = 484
232 = 529
242 = 576
252 = 625

4. What is a square root? 5 and 5 Two identical factors of a number.
What if it is a Non-Perfect Square????
How do you find the two identical factors?
5 and 5

5. Rationalizing
We are going to “simplify” the radical (square root #) as much as possible.
Find the square root of 20.
Think about what “PERFECT SQUARES” are factors of 20.
The only perfect square factor is 4.
4 times 5 equals 20.

6. Rationalizing continued…
What is the square root of 4? 2
We can simplify the square root of 20 to

7. Prove that this is true…
2 • 2 = 4
4 • 5 = 20

8. Find the This is not a perfect square.
Think of all the perfect square factors:
16 times 3
4 times 12 (12 is really 4 times 3)
The BEST perfect square factor is 16.

9. Find the This is not a perfect square.
Think of all the perfect square factors:
100 times 2
25 times 8 (8 is really 4 times 2)
The BEST perfect square factor is 100.

10. Rationalize the following: