Questions on 7.3 HW? (Beware: Even if you don’t ask, I’m going to go through some 7.3 problems that students usually have trouble with before we start the new material…)Slide 2The key to many of the problems in section 7.3 is to break the numbers down into their prime factors. Just start dividing the number under the radical by the smallest prime numbers (2, 3, 5, 7), and then keep breaking down the result further until you get to all primes.Slide 4Slide 5Slide 6Slide 7Slide 8Section 7.4 ASlide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Reminder:Slide 25Questions on 7.3 HW?(Beware: Even if you don’t ask, I’m going to go through some 7.3 problems that students usually have trouble with before we start the new material…)Now pleaseCLOSE YOUR LAPTOPSand turn off and put away your cell phones.Sample Problems Page Link(Dr. Bruce Johnston)The key to many of the problems in section 7.3 is to break the numbers down into their prime factors.Just start dividing the number under the radical by the smallest prime numbers (2, 3, 5, 7), and then keep breaking down the result further until you get to all primes.To start: What number goes into 250? (There is more than one right answer to this.)Example: 5 goes into 250, leaving 50 as the other factor.Then divide 5 into 50 again, leaving 10.Finally, factor 10 into 2 times 5.The complete factoring of 250 is then 5∙5∙5∙2, or 2∙53Now 3 2250 2 5 5 2 5 5 2 5 5 10= � = ��= �=3 333250 2 5 5 2= � =Section 7.4 AAdding and Subtracting Radical Expressionsnnnbaab 0 if nnnnbbabaRecall the product and quotient rules from yesterday’s lecture:: 400 4 100 4 100 2 10 20Example = = = =g g g3 3:16 416x x x xExample = =Rules in the previous section allowed us to split radicals that had a radicand which was a product or a quotient.We can NOT split sums or differences.a b a b+ � +a b a b- � -THIS IS IMPORTANT!!!!!THIS IS IMPORTANT!!!!!To show that 9 16 9 16 :9 16 25 5.9 16 3 4 7+ � ++ = =+ = + =Examples with Numbers:•In previous chapters, we’ve discussed the concept of “like” terms.•These are terms with the same variables raised to the same powers.•They can be combined through addition and subtraction.Example: (x2 + 5x – 1) + (6x2 - 3x + 4) = 7x2 + 2x + 3•Similarly, we can work with the concept of “like” radicals to combine radicals with the same radicand.•Like radicals are radicals with the same index and the same radicand.•Like radicals can also be combined with addition or subtraction by using the distributive property. 37338 242102632 42 Can not simplify (different indices)35 Can not simplify (different radicands)ExampleAlways simplify radicals FIRST to determine whether there are like radicals to be combined.Simplify the following radical expression. 331275 3334325 3334325 333235  332536ExampleSimplify the following radical expression. 9146433 91443 3145 ExampleSimplify the following radical expression. Assume that variables represent positive real numbers. xxx 54533 xxxx 55932 xxxx 55932 xxxx 5533 xxxx 559  xxx 59xx 510Example3:11 3Answer:14Answer x x36:12Answer -Reminder:This homework assignment on section 7.4A is due at the start of next class period.You may now OPEN your LAPTOPSand begin working on the homework