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PREC11 Unit4 notes - PRE-CALCULUS 11 Unit 4 Day 1 WORKING...

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PRE-CALCULUS 11 Unit 4 – Day 1: WORKING WITH RADICALS RADICALS Radicals are expressions in the form n a , which is the " n th root of a ". is the radical symbol; n is the index; and a is the radicand. n a = a number such that (the number) n = a 25 = because 3 8 = because 4 81 = because The index, n , must be a positive integer. Restrictions on Radicands - 25 = a number only if (the number) 2 = - 25 There is no real number that will satisfy this condition, - 25 is not a real number. When the index of a radical is even, the radicand must be greater than or equal to zero and the radical is positive. - 3 8 = a number only if (the number) 3 = - 8 - 3 8 is the negative number - 2. When the index of a radical is odd, the radicand could be any real number: o If the radicand is positive, then the radical is positive, o If the radicand is negative, then the radical is negative. exercise: For what values of x is x - 7 3 a real value? [ Answer: x 7 3 ] exercise: For what values of x is x 2 a real number? [ Answer: x R ] exercise: Does x 2 = x for all values of x ? [ Answer: x 0 ]
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Unit 4: Day 1 notes - Working with Radicals Page 2 of 2 SIMPLIFYING SQUARE ROOTS There are rules that can be used to work with radicals. n ab = ( n a ( n b n a b = n n a b m n a = m n a The first condition for simplest radical form with square roots is: ° the radicand cannot have a factor that is perfect square larger than 1. example: Simplify 72 Just simplify 72 (36)(2) ( 36 ( 2 Answer: 6 2 An entire radical is an expression that is only a radical; 72 . A mixed radical is an expression that is a product of a non-radical and a radical; 6 2 . exercise: For a 0 and b 0 , simplify 6 9 48 a b [ Answer: 3 4 4 3 a b b ] exercise: Simplify 3 40 [ Answer: 3 2 5 ] ADDING AND SUBTRACTING RADICALS Adding/subtracting monomial terms: only like terms can be combined. 7 x + 5 y + 9 x simplifies to 16 x + 5 y Adding/subtracting radical terms: only terms with the same radical can be combined.
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