1. 10/29/12 Unit 2Triangles Right Triangles I can….. simplify radical expressions.

2. In the expression, is the radical sign and 64 is the radicand. 1. Find the square root: 8

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

4. How do you know when a radical problem is done? 1. No radicals can be simplified. Example: 2. There are no fractions in the radical. Example: 3. There are no radicals in the denominator. Example:

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

6. Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324 400… 289

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,...

8. = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

9. Simplify 1.. 2.. 3.. 4..

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

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

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

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

14. Simplify 1. 3x 6 2. 3x 18 3. 9x 6 4. 9x 18

15. 6. Simplify Multiply the radicals.

16. 7. Simplify Multiply the coefficients and radicals.

17. Simplify 1.. 2.. 3.. 4..

18. 8. Simplify. Divide the radicals. Uh oh… There is a radical in the denominator! Whew! It simplified!

19. 9. Simplify Uh oh… Another radical in the denominator! Whew! It simplified again! I hope they all are like this!

20. 10. Simplify Since the fraction doesn’t reduce, split the radical up. Uh oh… There is a fraction in the radical! How do I get rid of the radical in the denominator? Multiply by the “fancy one” to make the denominator a perfect square!