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Chapter 11, Section 1: Square Root and Irrational Numbers

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- 1. Warm Up Simplify: 7 ² = 3.5 ² = 15 ² = 0.4 ² = 49 12.25 225 0.16
- 2. Chapter 11, Section 1 Square Roots and Irrational Numbers By Ms. Dewey-Hoffman
- 3. Area of a Square The area of a square is the SQUARE of the length of a side. (s²) The square of an integer is a perfect square . Example: 2² = 4 (4 is a perfect square ) 4² = 16 (16 is a perfect square )
- 4. Everything in Math has an Opposite The opposite of a SQUARE is a SQUARE ROOT . The symbol: √ indicates a NONNEGATIVE Square Root of a number. Square Root = Radical Same thing!!!
- 5. Examples Simplify each Square Root: √ 64 = ? -√121 = ? √ 100 = ? -√16 = ? 8 -11 10 -4
- 6. 13 Perfect Squares 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, and 144. Recommend Memorizing.
- 7. Estimating Non-Perfect Squares For Integers that are NOT perfect squares, you can estimate a square root. √ 4 √ 9 2 2.5 3 √ 8 = 2.83
- 8. Estimating Square Roots to the Nearest Integer. √ 15 -> Look for the two perfect squares on either side of 15. √ 9 < √15 < √16 -> 15 is closer to 16. √ 16 = 4 Square root of 15 is close to 4. √ 15 ≈ 4 √ 15 = 3.87...
- 9. Estimate to the Nearest Integer √ 27 = -√72 = √ 50 = -√22 = 5 -8 7 -5
- 10. Classifying Real Numbers RATIONAL Numbers as the RATIO of two integers: decimals and fractions. But the decimal either repeats or terminates. IRRATIONAL Numbers CANNOT be expressed as a ratio and NEITHER repeat nor terminate. Positive Integer not a Perfect Square? Then the square root is irrational.
- 11. Identifying Rational or Irrational √ 18 = irrational, 18 not a perfect square √ 121 = rational, 121 is a perfect square -√24 = irrational, 24 not a perfect square 432.8 = rational, terminating decimal 0.1212... = rational, repeating decimal 0.120120012... = irrational π = irrational
- 12. Identify Each √ 2 = rational or irrational -√81 = rational or irrational 0.53 = rational or irrational √ 42 = rational or irrational
- 13. Assignment #30 Pages 562-563: 2-34 even #s, 39-45 all.

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