Download File - MATH by M Younts

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