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

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

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

4. 6.82, -6.82 6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth.

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

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

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

8. Simplify 1.. 2.. 3.. 4..

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

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

11. Simplify 1.3x 6 2.3x 18 3.9x 6 4.9x 18

12. What are Perfect Cubes? 1 3 = 1 x 1 x 1 = 1 2 3 = 2 x 2 x 2 = 8 3 3 = 3 x 3 x 3 = 27 4 3 = 4 x 4 x 4 = 64 5 3 = 5 x 5 x 5 = 125 and so on and on and on…..

13. 2 2 2 x 2 = 4

14. 3 x 3 = 9 3 3

15. 4 x 4 = 16 4 4

16. 5 5 5 x 5 = 25

17. The square root of 4 is 2

18. The square root of 9 is 3

19. The square root of 16 is 4

20. The square root of 25 is 5

21. 12 34 56 78 Cubes

22. 2 2 2 2 x 2 x 2 = 8

23. 3 x 3 x 3 = 27

24. 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:

25. SIMPLIFY 1. 2. 3.

26. ANSWERS 1.7 2.-2 3.3xy 2

27. 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?

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