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I can classify real numbers I can plot real numbers on the number line and order real numbers.

Goal. I can classify real numbers I can plot real numbers on the number line and order real numbers. I can calculate perfect squares and square roots. With a partner, list examples of as many different types of numbers as you can think of. Irrational Numbers. √2 pi √3. Rational Numbers.

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I can classify real numbers I can plot real numbers on the number line and order real numbers.

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  1. Goal • I can classify real numbers • I can plot real numbers on the number line and order real numbers. • I can calculate perfect squares and square roots

  2. With a partner, list examples of as many different types of numbers as you can think of.

  3. Irrational Numbers √2 pi√3 Rational Numbers ½ 1/3 ¼ 13/8 1.673 Integers Natural Numbers: 1,2,3,… -2 -1 0 Real Numbers • Integers: Positive and Negative Natural Numbers (and 0) • Rational Numbers: Fractions of Integers, Decimals with repeating patterns. • Irrational Numbers: Have infinite decimal expansions with no patterns

  4. The Real Number System • Irrational • numbers • Cannot be • represented • as a fraction • of 2 integers • Rational numbers • Can be represented as a fraction of 2 integers Integers .… -3, -2, -1, 0, 1, 2, 3, …. Whole numbers 0, 1, 2, 3, …. Natural numbers 1, 2, 3, ….

  5. notes Squares & Square Roots PART I: Perfect Squares DEFINITION: the square of a whole number

  6. notes Square Number • Also called a “perfect square” • A number that is the square of a whole number (Can be represented by arranging objects in a square.)

  7. Square Numbers

  8. notes Square Numbers • 1 x 1 = 1 • 2 x 2 = 4 • 3 x 3 = 9 • 4 x 4 = 16

  9. notes Square Numbers • 1 x 1 = 1 • 2 x 2 = 4 • 3 x 3 = 9 • 4 x 4 = 16 Activity: You have 2 minutes! In your notes: Calculate the perfect squaresup to 152…

  10. notes Square Numbers • 9 x 9 = 81 • 10 x 10 = 100 • 11 x 11 = 121 • 12 x 12 = 144 • 13 x 13 = 169 • 14 x 14 = 196 • 15 x 15 = 225 • 1 x 1 = 1 • 2 x 2 = 4 • 3 x 3 = 9 • 4 x 4 = 16 • 5 x 5 = 25 • 6 x 6 = 36 • 7 x 7 = 49 • 8 x 8 = 64

  11. notes Squares & Square Roots PART II: Square Root DEFINITION: the length of the side of a square with an area equal to a given number RADICAL SIGN √ : used to represent a square root

  12. Are squares and square roots inverses? Start Root it Square it Result 3 3 5 5 9 9 A square root is the inverse operation of a square!

  13. Square Numbers • One property of a perfect square is that it can be represented by a square array. • Each small square in the array shown has a side length of 1cm. • The large square has a side length of 4 cm. 4cm 4cm 16 cm2

  14. notes Square Root • A number which, when multiplied by itself, results in another number. • Ex: 5 is the square root of 25. 5 = 25

  15. notes Finding Square Roots • Quick Steps: Find… 64 • STEP 1:THINK … What # to the 2nd power EQUALS the # inside of the radical? ___² = 64 • STEP 2:Double check your answer with multiplication. Multiply the BASE X BASE. 8 X 8 = 64 so the square root of 64 = 8

  16. notes Squares & Square Roots Estimating Square Root NON PERFECT SQUARE - a # that when squared is not a whole #. EX: 6 is a non perfect square because √6 is a DECIMAL

  17. Estimating Square Roots 27 = ? Since 27 is not a perfect square, we have to use another method to calculate it’s square root.

  18. notes Estimating Square Roots • Not all numbers are perfect squares. • Not every number has an Integer for a square root. • We have to estimate square roots for numbers between perfect squares.

  19. notes Estimating Square Roots • To calculate the square root of a non-perfect square STEP 1: Place the values of the adjacent perfect squares on a number line. STEP 2: Interpolate between the points to estimate to the nearest tenth.

  20. notes Estimating Square Roots • Example: 27 What are the perfect squares on each side of 27? 5 6 √25 √36

  21. Estimating Square Roots • Example: 27 half 5 6 √25 30 35 √36 27 Estimate 27 = 5.2

  22. Estimating Square Roots • Example: 27 • Estimate: 27 = 5.2 • Check: (5.2) (5.2) = 27.04

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