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Name Class Date Practice Form K Roots and Radical Expressions Find all the real square roots of each number. 1. 625 2. -1.44 16 3. 81 Find all the real cube roots of each number. 4. -216 1 5. 64 6. 0.027 Find all the real fourth roots of each number. 7. 0.2401 9. -1296 8. 1 Find each real root. To start, fi nd a number whose square, cube, or fourth is equal to the radicand. 10. 1400 = 2(20)2 4 11. - 1256 3 12. 1 -729 Simplify each radical expression. Use absolute value symbols when needed. To start, write the factors of the radicand as perfect squares, cubes, or fourths. 13. 225x 6 = 2(5)2(x3)2 3 14. 2343x 9y 12 4 15. 216x 16y 20 Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. Name Class Date Practice (continued) Form K Roots and Radical Expressions 3 16. The formula for the volume of a sphere is V = 4 3 pr . Solving for r, the radius of 3 3V 3 a sphere is r = 5 4p . If the volume of a sphere is 20 ft , what is the radius of the sphere to the nearest hundredth? Find the two real solutions of each equation. 17. x4 = 81 2401 19. x4 = 625 18. x2 = 144 20. Writing Explain how you know whether or not to include the absolute value symbol on your root. 3 3 6 21. Arrange the numbers 1 -64, - 1 -64, 164, and 164, in order from least to greatest. 22. Open-Ended Write a radical that has no real values. 23. Reasoning There are no real nth roots of a number b. What can you conclude about the index n and the number b? Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. Name Class Date Practice Form G Roots and Radical Expressions Find all the real square roots of each number. 2. -196 1. 400 3. 10,000 4. 0.0625 7. -0.064 1000 8. 27 Find all the real cube roots of each number. 6. -343 5. 216 Find all the real fourth roots of each number. 9. -81 10. 256 11. 0.0001 12. 625 14. - 125 15. 1-0.01 16. 10.001 Find each real root. 13. 1144 4 17. 10.0081 3 3 3 18. 127 19. 1 -27 20. 10.09 Simplify each radical expression. Use absolute value symbols when needed. 21. 281x 4 3 22. 2121y 10 5 3 23. 28g 6 3 24. 2125x 9 25. 2243x 5y 15 27. 225(x + 2)4 28. 5343 29. 1 -0.008 31. 236x 2y 6 32. 2(m - n)4 4 x4 30. 581 3 64x9 26. 2(x - 9)3 3 4 33. A cube has volume V = s3 , where s is the length of a side. Find the side length for a cube with volume 8000 cm3. 34. The temperature T in degrees Celsius ( °C ) of a liquid t minutes after heating is given by the formula T = 8 1t. When is the temperature 48°C? Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. Name Class Date Practice (continued) Form G Roots and Radical Expressions Find the two real solutions of each equation. 35. x2 = 4 36. x4 = 81 37. x2 = 0.16 16 38. x2 = 49 16 39. x4 = 625 40. x2 = 121 625 41. x2 = 0.000009 42. x4 = 0.0001 43. The number of new customers n that visit a dry cleaning shop in one year is directly related to the amount a (in dollars) spent on advertising. This relationship is represented by n3 = 13,824a. To attract 480 new customers, how much should the owners spend on advertising during the year? 44. Geometry The volume V of a sphere with radius r is given by the formula V = 43 pr 3 . a. What is the radius of a sphere with volume 36p cubic inches? b. If the volume increases by a factor of 8, what is the new radius? 45. A clothing manufacturer finds the number of defective blouses d is a function of the total number of blouses n produced at her factory. This function is d = 0.000005n2 . a. What is the total number of blouses produced if 45 are defective? b. If the number of defective blouses increases by a factor of 9, how does the total number of blouses change? 46. The velocity of a falling object can be found using the formula v 2 = 64h, where v is the velocity (in feet per second) and h is the distance the object has already fallen. a. What is the velocity of the object after a 10-foot fall? b. How much does the velocity increase if the object falls 20 feet rather than 10 feet? Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.