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Chapter 11, Section 1 Square Roots and Irrational Numbers By Ms. Dewey-Hoffman
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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 )
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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!!!
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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
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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...
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Estimate to the Nearest Integer √ 27 = -√72 = √ 50 = -√22 = 5 -8 7 -5
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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.
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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
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Identify Each √ 2 = rational or irrational -√81 = rational or irrational 0.53 = rational or irrational √ 42 = rational or irrational
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Assignment #30 Pages 562-563: 2-34 even #s, 39-45 all.
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