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Simplifying Non-Perfect Squares

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. Know Perfect Squares. 1 2 = 1 2 2 = 4 3 2 = 9

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Simplifying Non-Perfect Squares

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  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.

  3. Know Perfect Squares • 12 = 1 • 22 = 4 • 32 = 9 • 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? • 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:

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