Simplifying Radicals: Techniques and Practice Problems

Learn how to simplify radicals by finding square roots and simplifying radical expressions. Practice finding square roots of various numbers, identifying perfect squares, simplifying variables in radicals, and more. Graph inequalities and solve problems step by step.

• Radicals
• Square Roots
• Simplification Techniques
• Inequalities
• Practice Problems

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1. 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; + 2 6 1 13 X X

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

3. If x2 = y then x is a square root of y. In the expression , is the radical sign and 64 is the radicand. 64 64 1. Find the square root: 8 0.04 2. Find the square root: -0.2

4. 3. Find the square root: 121 11, -11 441 4. Find the square root: 21 25 81 5. Find the square root: 5 9

5. 6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth. 46.5 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 147 Find a perfect square that goes into 147. 147 = 147 = 147 = 49 49 7 3 3 3

8. 2. Simplify 605 Find a perfect square that goes into 605. 121 5 121 11 5 5

9. 72 Simplify 1. . 2. . 3. . 4. . 2 18 3 8 6 2 36 2

10. How do you simplify variables in the radical? x7 Look at these examples and try to find the pattern = 2x x = 3x x x = 4 2 x x = 5 2 x x x = 6 3 x x = 1x x7 x What is the answer to ? = 7 3 x x x As a general rule, divide the exponent by two. The remainder stays in the radical.

11. 4. Simplify 49x2 Find a perfect square that goes into 49. 2 49 x 7x 5. Simplify 25 8x 25 4 2x 12 x 2 2 x

12. 36 Simplify 9x 1. 3x6 2. 3x18 3. 9x6 4. 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. The square root of 4 is 2

19. The square root of 9 is 3

20. The square root of 16 is 4

21. The square root of 25 is 5

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. n 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: 3 4 5

26. SIMPLIFY 343 8 3 1. 2. 3 3. 3 6 3 27 x y

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? = 2 3 a P

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.