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Simplifying Radicals for Beginners: Learn and Practice Step by Step

Explore how to simplify square roots and radical expressions efficiently, with step-by-step examples and calculator usage. Discover perfect squares, cubes, and nth roots, enhance your skills, and solve inequalities effectively. Practice and master the basics of radicals now!

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Simplifying Radicals for Beginners: Learn and Practice Step by Step

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  1. Simplify Radicals www.assignmentpoint.com

  2. DO NOW: SOLVE THE INEQUALITY BY FOLLOWING THE STEPS WE HAVE LEARNED OVER THE LAST TWO DAYS. THEN WE WILL GRAPH TOGETHER ON THE CALCULATOR; www.assignmentpoint.com

  3. HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions. www.assignmentpoint.com

  4. If x2 = y then x is a square rootof y. In the expression , is the radical signand64 is the radicand. 1. Find the square root: 8 2. Find the square root: -0.2 www.assignmentpoint.com

  5. 3. Find the square root: 11, -11 4. Find the square root: 21 5. Find the square root: www.assignmentpoint.com

  6. 6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth. 6.82, -6.82 www.assignmentpoint.com

  7. What numbers are perfect squares? 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 49, 64, 81, 100, 121, 144, ... www.assignmentpoint.com

  8. 1. Simplify Find a perfect square that goes into 147. www.assignmentpoint.com

  9. 2. Simplify Find a perfect square that goes into 605. www.assignmentpoint.com

  10. Simplify • . • . • . • . www.assignmentpoint.com

  11. How do you simplify variables in the radical? What is the answer to ? Look at these examples and try to find the pattern… As a general rule, divide the exponent by two. The remainder stays in the radical. www.assignmentpoint.com

  12. 4. Simplify Find a perfect square that goes into 49. 5. Simplify www.assignmentpoint.com

  13. Simplify • 3x6 • 3x18 • 9x6 • 9x18 www.assignmentpoint.com

  14. 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 • and so on and on and on….. www.assignmentpoint.com

  15. 2 x 2 = 4 2 2 www.assignmentpoint.com

  16. 3 x 3 = 9 3 3 www.assignmentpoint.com

  17. 4 x 4 = 16 4 4 www.assignmentpoint.com

  18. 5 x 5 = 25 5 5 www.assignmentpoint.com

  19. 2 The square root of 4 is www.assignmentpoint.com

  20. 3 The square root of 9 is www.assignmentpoint.com

  21. 4 The square root of 16 is www.assignmentpoint.com

  22. 5 The square root of 25 is www.assignmentpoint.com

  23. Cubes 5 6 7 8 1 2 3 4 www.assignmentpoint.com

  24. 2 x 2 x 2 = 8 2 2 2 www.assignmentpoint.com

  25. 3 x 3 x 3 = 27 www.assignmentpoint.com

  26. NTH ROOTS • a square (second) root is written as: • a cube (third) root is written as: • a fourth root is written as:  • a fifth root is written as:  www.assignmentpoint.com

  27. SIMPLIFY 1. 2. 3. www.assignmentpoint.com

  28. ANSWERS • 1. 7 • 2. -2 • 3. 3xy2 www.assignmentpoint.com

  29. CUBES: Cathy is building a cubic storage room. She wants the volume of the space to be 1728 cubic feet. What should the dimensions of the cube be? www.assignmentpoint.com

  30. ASTRONOMY A special form of Kepler’s Third Law of Planetary Motion is given by where a is the average distance of an object from the Sun in AU (astronomical units) and P is the period of the orbit in years. If an object is orbiting the Sun with a period of 12 years, what is its distance from the Sun? www.assignmentpoint.com

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