Simplifying Non-Perfect Squares

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Presentation transcript:

Simplifying Non-Perfect Squares

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.

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

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

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.

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

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

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.

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.

Rationalize the following: