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7 White 1.6 Notes Square & Cube Roots Perfect Squares The square of an integer is called a ____________________________. Generate the first 10 perfect squares below: 2 2 2 2 2 1 2 3 4 5 62 72 82 92 102 _____, _____, _____, _____, _____, _____, _____, _____, _____, _____ Square Roots • The opposite of squaring a number is finding the _____________________. • Positive numbers have _______ square roots. Ø Why? What number(s) can you square to get 16? ______________ • Negative numbers have __________ square roots. • What number only has one square root? ________ Radical Notation • The radical sign, 𝑥, is used to indicate the square root of 𝑥. Ø 𝑥 is used to indicate the _________________ square root of 𝑥. Ø − 𝑥 is used to indicate the _________________ square root of 𝑥. Find each square root. EXAMPLES Perfect vs. Non-Perfect SQUARES 1. 49 4. 484 2. − 4 5. − )* +, 3. − 196 6. -. *-- Directions: CIRCLE each value that is a perfect square. 9 32 50 121 1 160 64 200 324 If a number is not a perfect square, it’s called a non-perfect square. ESTIMATING Non-Perfect Square Roots Identify the two consecutive integers in which each square root lies between. 8. − 41 9. − 206 7. 115 Approximate each square root to the nearest tenth. 10. 84 11. − 27 12. 145 Perfect Cubes Cube Roots The cube of an integer is called a ____________________________. Generate the first 10 perfect cubes below: 3 3 3 3 3 1 2 3 4 5 63 73 83 93 103 _____, _____, _____, _____, _____, _____, _____, _____, _____, _____ • The opposite of cubing a number is finding the _____________________. • ALL integers have only _______ cube root. Ø Why? What number(s) can you cube to get 8? ____________ What number(s) can you cube to get -8? ___________ 3 • The radical sign, 𝑥 , is used to indicate the cube root of 𝑥. Find each cube root. EXAMPLES 3 14. 343 3 17. 3 −2,197 13. 64 16. −1 3 3 15. −27 3 18. 512