1. 9.3 Simplifying Radicals

2. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number a if b 2 = a. In order to find a square root of a, you need a # that, when squared, equals a.

3. 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 or -8

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

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

6. 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?

7. = 2 = 4 = 5 = 10 = 12

8. If and are real numbers, Product Rule for Radicals

9. Simplify the following radical expressions. No perfect square factor, so the radical is already simplified. Simplifying Radicals Example

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

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

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

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

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

15. Simplify 1.. 2.. 3.. 4..

16. * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

17. Multiply the radicals. 6. Simplify

18. 7. Simplify Multiply the coefficients and radicals.

19. Multiply and then simplify

21. 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:

22. To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that there are NO TENTS IN THE BASEMENT!

24. NO TENTS IN THE BASEMENT so…… Multiply the expression by DENOMINATOR DENOMINATOR to get rid of the radical in the basement

25. This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

26. This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. Reduce the fraction.

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

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

29. 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!