1. Objectives The student will be able to: 1. simplify square roots, and 2.simplify radical expressions. Designed by Skip Tyler, Varina High School

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. It is a number that has a whole number square root. What is a Perfect Square?

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

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

7. What are some strategies for finding the perfect squares in radicands? The square root is simplified when there are no perfect squares left in the radicand.

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

9. Compare and Contrast Find the square root of with your calculator. Now simplify the square root of This means 31 and 0.18 This means 18 times Are these answers equivalent?

10. Simplify 1.. 2.. 3.. 4..

11. 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.

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

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

14. Multiply the radicals. 6. Simplify

15. 7. Simplify Multiply the coefficients and radicals.

16. Simplify 1.. 2.. 3.. 4..

17. How do you know when a radical problem is done? 1.No perfect squares are in the radicand. Example: 2.There are no fractions in the radical. Example: 3.There are no radicals in the denominator. Example:

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

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

20. Simplify. Divide the radicals.

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

22. Simplify

23. 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 same square root to make the denominator a perfect square!

24. Simplify Multiply by the same square root to make the denominator a perfect square!

25. in two different ways. Simplify Describe which way you prefer and explain why.

26. Closure: Explain how you can tell if a radical expression is in simplified form.