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 Now please CLOSE YOUR LAPTOPS and 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 53 Now 3 2 250 2 5 5 2 5 5 2 5 5 10 3 3 3 250 2 5 5 2 3 Section 7 4 A Adding and Subtracting Radical Expressions Recall the product and quotient rules from yesterday s lecture n ab a b n n Example 400 4g100 4 g 100 2g10 20 n n a a n n if b 0 b b x3 x3 x x Example 16 4 16 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 THIS IS IMPORTANT a b a b a b a b THIS IS IMPORTANT Examples with Numbers To show that 9 16 9 16 9 16 25 5 9 16 3 4 7 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 Example 3 7 3 8 3 10 2 4 2 6 2 3 2 4 2 5 3 Can not simplify different indices Can not simplify different radicands Always simplify radicals FIRST to determine whether there are like radicals to be combined Example Simplify the following radical expression 75 12 3 3 25 3 4 3 3 3 25 3 4 3 3 3 5 3 2 3 3 3 5 2 3 3 6 3 Example Simplify the following radical expression 3 64 3 14 9 3 3 4 14 9 5 14 Example Simplify the following radical expression Assume that variables represent positive real numbers 3 2 3 45 x x 5 x 3 9 x 5 x x 5 x 3 9 x 2 5x x 5x 3 3 x 5 x x 5 x 9 x 5x x 5x 9x x 5 x 10 x 5 x 3 Answer 11 3 Answer 14 x x 3 6 Answer 12 Reminder This homework assignment on section 7 4A is due at the start of next class period You may now OPEN your LAPTOPS and begin working on the homework assignment
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