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HOW DO WE SIMPLIFY RADICALS?

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;. HOW DO WE SIMPLIFY RADICALS?. 1. simplify square roots, and 2. simplify radical expressions. If x 2 = y then x is a square root of y.

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HOW DO WE SIMPLIFY RADICALS?

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  1. 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;

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

  3. 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

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

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

  6. 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, ...

  7. 1. Simplify Find a perfect square that goes into 147.

  8. 2. Simplify Find a perfect square that goes into 605.

  9. Simplify • . • . • . • .

  10. 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.

  11. 4. Simplify Find a perfect square that goes into 49. 5. Simplify

  12. Simplify • 3x6 • 3x18 • 9x6 • 9x18

  13. 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…..

  14. 2 x 2 = 4 2 2

  15. 3 x 3 = 9 3 3

  16. 4 x 4 = 16 4 4

  17. 5 x 5 = 25 5 5

  18. 2 The square root of 4 is

  19. 3 The square root of 9 is

  20. 4 The square root of 16 is

  21. 5 The square root of 25 is

  22. Cubes 5 6 7 8 1 2 3 4

  23. 2 x 2 x 2 = 8 2 2 2

  24. 3 x 3 x 3 = 27

  25. 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: 

  26. SIMPLIFY 1. 2. 3.

  27. ANSWERS • 1. 7 • 2. -2 • 3. 3xy2

  28. 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?

  29. 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?

  30. This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.

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