1. 1. Simplifying Radicals
2. 2. Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324 400 625 289
3. 3. 4 16 25 100 144 = 2 = 4 = 5 = 10 = 12
4. 4. 8 20 32 75 40 = = = = = 2*4 5*4 2*16 3*25 10*4 = = = = = 22 52 24 35 102 Perfect Square Factor * Other Factor LEAVEINRADICALFORM
5. 5. 48 80 50 125 450 = = = = = 3*16 5*16 2*25 5*25 2*225 = = = = = 34 54 25 55 215 Perfect Square Factor * Other Factor LEAVEINRADICALFORM
6. 6. + To combine radicals: combine the coefficients of like radicals
7. 7. Simplify each expression =+ 737576 78 =++ 62747365 7763 +
8. 8. Simplify each expression: Simplify each radical first and then combine. = 323502 22 212210 24*325*2 2*1632*252 = = =
9. 9. Simplify each expression: Simplify each radical first and then combine. =+ 485273 329 32039 34*533*3 3*1653*93 =+ =+ =+
10. 10. 18 288 75 24 72 = = = = = = = = = = Perfect Square Factor * Other Factor LEAVEINRADICALFORM
11. 11. Simplify each expression =+ 636556 =+ 547243 = 32782
12. 12. Simplify each expression =+ 20556 =+ 32718 =+ 6367282
13. 13. * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.
14. 14. =35*5 =175 =7*25 75 Multiply and then simplify =73*82 =566 =14*46 =142*6 1412 =204*52 =10020 20010*20 =
15. 15. ( ) = 2 5 =5*5 =25 5 ( ) = 2 7 =7*7 =49 7 ( ) = 2 8 =8*8 =64 8 ( ) = 2 x =xx * =2 x x
16. 16. To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator
17. 17. = 7 56 =8 =2*4 22
18. 18. = 7 6 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. = 7 7 * 7 6 = 49 42 7 42 42 cannot be simplified, so we are finished.
19. 19. 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. = 10 5 = 2 2 * 2 1 10 2
20. 20. 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. = 12 3 = 3 3 * 12 3 = 36 33 = 6 33 6 3 Reduce the fraction.
21. 21. 2 X 6 Y 264 YXP 24 4 YX 108 25 DC = X = Y3 = P2 X3 Y = 2X2 Y = 5C4 D10
22. 22. 3 X XX = = XX *2 YY 45 Y = = YY 2
23. 23. 33 YPX 27 12 YX 98 25 DC = = = 5 Y PXYYX *22 5 Y PXYXY=