This document discusses square roots and irrational numbers. It defines a square root as the opposite of a square, and provides examples of simplifying square roots. It also discusses estimating square roots when they are not perfect squares, and classifying numbers as rational or irrational. Some key points are: - The square root of a number is the opposite of squaring it. Square roots are indicated with the radical symbol. - Perfect squares are integers that when squared result in another integer, like 4, 9, 16. - Square roots that do not result in a perfect square can be estimated by looking at the closest perfect squares. - Real numbers are either rational (can be expressed as a ratio of

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.