Perfect and Square Roots PDF

Name: Date: ___________________________________________________ _________________________________ Topic: Class: _____________...

Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples perfect The square of an integer is called a _________________ ________________. squares Generate the first 10 perfect squares below: 2 2 2 2 2 2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 _______, _______, _______, _______, _______, _______, _______, _______, _______, _______ SQUARE ROOTS The opposite of squaring a number is finding the _____________ __________. Positive numbers have ________ square roots.
Why? What number(s) can you square to get 16? _______________ Negative numbers have __________ square roots. What number only has one square root? _______ The radical sign, x , is used to indicate the square root of x. RADICAL
x is used to indicate the ________________ square root of x. notation
− x is used to indicate the ________________ square root of x. Directions: Find each square root. Examples 1. 49 2. 9 3. − 4 4. − 289 5. − 196 6. 484 1 81 49 7. 8. − 9. 16 25 144 Directions: CIRCLE each value that is a perfect square. PERFECT VS. NON-PERFECT 9 32 50 121 1 160 64 200 324 Squares If a number is not a perfect square, it’s called a non-perfect square. © Gina Wilson (All Things Algebra), 2016  Directions: Identify the two consecutive integers in which each square root lies Estimating between. 10. 10 11. 115 12. 59 NON-PERFECT square roots 13. − 41 14. − 3 15. − 206 Directions: Approximate each square root to the nearest tenth. 16. 84 17. − 27 18. 145 perfect The cube of an integer is called a _________________ ________________. CUBES Generate the first 10 perfect cubes below: 3 3 3 3 3 3 3 3 3 3 1 2 3 4 5 6 7 8 9 10 _______, _______, _______, _______, _______, _______, _______, _______, _______, _______ The opposite of cubing a number is finding the ____________ ___________. CUBE ROOTS ALL integers have only ________ cube root.
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. Directions: Find each cube root. Examples 19. 3 64 20. 3 343 21. 3 −27 3 3 3 22. −1 23. −2,197 24. 512 Summary: ______________________________________________________________________________________________ __________________________________________________________________________________________________________ __________________________________________________________________________________________________________ __________________________________________________________________________________________________________ © Gina Wilson (All Things Algebra), 2016 Name: ___________________________________ Unit 1: The Real Numbers Date: ________________________ Per: ______ Homework 6: Square and Cube Roots 1. Circle each value that is a perfect square. 50 81 289 360 4 100 75 224 25 Directions: Find each square root. 2. 36 3. − 225 4. − 64 5. 324 6. 121 7. − 169 16 81 1 8. 9. 10. − 9 400 100 Directions: Identify the two consecutive integers in which each square root lies between. 11. 95 12. 320 13. − 17 14. − 156 15. 48 16. − 249 Directions: Estimate each square root to the nearest tenth. 17. 108 18. − 372 19. 61 20. Circle each value that is a perfect cube. 27 1,000 90 1 300 72 525 216 Directions: Find each cube root. 3 3 3 21. 729 22. 125 23. −1, 331 24. Explain why each non-zero integer has two square roots but only one cube root. _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ © Gina Wilson (All Things Algebra), 2016 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples Scientific notation is a _________________ way of writing very ____________ Scientific or very ______________ numbers. Notation A number written in scientific notation has the form a × 10 where n 1 ≤ a < 10. Step 1: Move the decimal so the new number is between 1 and a number Converting up to 10. to Scientific Step 2: Write using a power of ten. The exponent matches the number of Notation times the decimal was moved. If the decimal was moved ___________, the exponent is __________________. If the decimal was moved ___________, the exponent is __________________. Directions: Write each number in scientific notation. Standard Form Scientific Notation 1. 540 2. 937,000 3. 1, 852,000 4. 76, 820 5. 4,671 6. 0.00982 7. 0.05273 8. 0.0000014 9. 0.258 10. 0.00000000725 Directions: Determine if the number is correctly written in scientific notation. If not, correct it. 7 3 11. 2.98 × 10 12. 11.4 × 10 −5 −2 13. 85.1 × 10 14. 6.7 × 10 © Gina Wilson (All Things Algebra), 2016