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PURPOSE 1. Seated and Silent by 7:53. 2. Have forms ready to turn in. 3. Have Student Survey ready to turn in. 4. Complete All About Me Assignment or Time Capsule Activity if not completed yesterday. 5. All About Me and Time Capsule are on the back counter. 6. Today we will be discussing TCAP scores. Advisory – Silent Reading If you do not have your own reading material, take a book, magazine, comic, or graphic novel from my shelf. Procedures Review • Think of at least 3 procedures we talked about yesterday. • Be prepared to share one of those procedures if your UNO card is drawn. Square Roots, Cube Roots, and Irrational Numbers 8.EE.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. Words to know… • • • • Square root Perfect square Irrational Cube root Individual Think Time: How can you turn two blocks into a square? 2x2=4 2 2 3x3=9 3 3 4 x 4 = 16 4 4 5 x 5 = 25 5 5 The square root of 4 is 2 The square root of 9 is 3 The square root of 16 is 4 The square root of 25 is 5 Square numbers Here are the first 10 square numbers: 12 = 1 × 1 = 1 22 = 2 × 2 = 4 32 = 3 × 3 = 9 42 = 4 × 4 = 16 52 = 5 × 5 = 25 62 = 6 × 6 = 36 72 = 7 × 7 = 49 82 = 8 × 8 = 64 92 = 9 × 9 = 81 102 = 10 × 10 = 100 Adding consecutive odd numbers The tenth first square second third fourth fifth sixth seventh eighth ninth square square square square square square number number number number number number number is isis isis 1. 25. is 9. 36. 100. 81. is16. 64. 4.49. 1+3+ = 54 + = 79 + =9 16+ = 11 25 + = 13 36 + = 15 49 + = 17 64 + = 19 81 = 100 Think about this….. Could you figure out what the 11th square number would be? Think about this….. What about the 15th square number? Square roots Finding the square root is the inverse of finding the square: squared 8 64 square rooted We write 64 = 8 The square root of 64 is 8. Square roots We can easily find the square root of a square number. 1 = 1 36 = 6 4 = 2 49 = 7 9 = 3 64 = 8 16 = 4 81 = 9 25 = 5 100 = 10 Square numbers When we multiply a number by itself we say that we are squaring the number. To square a number we can write a small 2 after it. For example, the number 3 multiplied by itself can be written as Three squared 3×3 or 32 The value of three squared is 9. The result of any whole number multiplied by itself is called a perfect square. Think about this…… 4 ? 9 49 ? 100 Think about this…… 4 2 9 3 49 7 100 10 Approximating Square Roots Square roots that are not perfect squares are called irrational. An irrational number in a non-repeating, non-terminating decimal. This means the decimal does not repeat, but it also doesn’t end. Remember Categorize the following square roots as rational or irrational. For example, the 4 is rational because 22 or 2 x 2 = 4. The 5 is irrational because there is no whole number that can be multiplied by itself to result in 5. 15 289 160 400 1 Think about this…. • What could be a square root that is irrational? • How do you know? Cubes 5 7 6 8 1 3 2 4 2x2x2=8 2 2 2 3 x 3 x 3 = 27 Cube Roots The index of a cube root is always 3. The cube root of 64 is written as 3 64 . What does cube root mean? The cube root of a number is… …the value when multiplied by itself three times gives the original number. Cube Root Vocabulary radical sign index n x radicand Perfect Cubes If a number is a perfect cube, then you can find its exact cube root. A perfect cube is a number that can be written as the cube (raised to third power) of another number. What are Perfect Cubes? • • • • • • 13 = 1 x 1 x 1 = 1 23 = 2 x 2 x 2 = 8 33 = 3 x 3 x 3 = 27 43 = 4 x 4 x 4 = 64 53 = 5 x 5 x 5 = 125 What would the next perfect cube be? Examples: 3 64 4 because 4 4 4 4 3 64 Examples: 27 3 3 216 6 3 64 4 125 5 3 3 3 3 27 3 216 6 64 4 125 5