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Simplifying Non-Perfect Squares

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43210 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 expressio ns 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. 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.

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Know Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 21 2 = 441 22 2 = 484 23 2 = 529 24 2 = 576 25 2 = 625 11 2 = 121 12 2 = 144 13 2 = 169 14 2 = 196 15 2 = 225 16 2 = 256 17 2 = 289 18 2 = 324 19 2 = 361 20 2 = 400

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What is a square root? 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

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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.

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

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

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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.

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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.

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Rationalize the following:

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