1. Simplifying Radicals

2. Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 400 625 Perfect Cubes 1 8 27 64 125 216 343 512 729 1000

3. 2 4 4 8 6 12

4. Find the largest Perfect Square Factor LEAVE IN RADICAL FORM

5. This time Prime Factor the radicand LEAVE IN RADICAL FORM

7. and

10. To combine radicals: combine the ______________ of __________ radicals coefficients like

11. Simplify each expression

12. Simplify each expression: Simplify each radical first (largest perfect square) and then combine.

14. To multiply radicals: multiply the _____________ and then multiply the _____________. Simplify the remaining radicals. radicands coefficients

15. Multiply and then simplify

17. To divide radicals: divide the____________, if possible divide the __________, if possible _________________ the denominator so that no radical remains in the denominator radicands coefficients Rationalize

19. 42 cannot be simplified, so we are finished. Rationalizing the denominator. This expression can not be divided which leaves a 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. Look back at slide #15

20. This can be divided, but this leaves a radical in the denominator. We do not radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

21. 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.