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# PRECALC ALG & TRIG MAC 1147

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This 10 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1147 at University of Florida taught by Larissa Williamson in Fall. Since its upload, it has received 43 views. For similar materials see /class/207048/mac-1147-university-of-florida in Calculus and Pre Calculus at University of Florida.

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Date Created: 09/19/15

L4 nth Roots Rational Exponents nth Roots A number I is an nth root of a number a if bquot a The principal nth root ofa real number a is denoted lt5 n 2 2 and defined as follows If n is an even number and a 2 0 then Q5 is the nonnegative nth root at lt 0 then d is undefined not a real number If n is an odd number then 75 is the only real nth root of a number a and it has the same sign as a Note Since 5 is an nth root then 45 a Example Evaluate the radical expressions 327 V5 32 31 l6 Cancellation Rule for Exponents and Radicals Wzla ifn22 andniseven a nza ifn23andnis0dd M xx 2 Example Simplify the expressions V4 34 xn0t ix 32 Rules for Radicals we assume that all radicals are defined n m n m n n n a quota HM magw mpg Simplify each expression 3 M39m 2 33 Simplifying Radicals 1 Use the cancellation rule for radicals and exponents to remove all possible factors out of the radical When it is done the factors left in the radicand will have smaller exponents than the indeX of the radical 6 2 2 Rationalize the denominator U3 le H Ls 3 Reduce the indeX of the radical as far as possible 4x2 ifoO 34 Example Simplify the expressions with radicals Assume that all variables are positive when they appear 324x5y7 4 32a5b7612 35 Caution x y 72 J J le y2 2 x y Addin and Subtractin Radical EX ressions We can only add or subtract like radicals Like radicals have the same index and the same radicand Example Add or subtract as indicated JEJ8 3 48x2y x l75y 33y xgt0ygt0 36 Rational Exponents If a is real and n 2 2 is an integer then a 4 provided that 3 is defined Note If n is even and a lt 0 then 4 and ai are not defined Example Simplify the expressions if possible 1 1445 1 1442 8g 37 If a i O is a real number and m and n are integers containing no common factors with n 2 2 then provided that lt5 is de ned Example Evaluate each expression 125g 1 E 16 38 Example Simplify the expressions Assume that all variables are positive when they appear 48x8 2 y 5 V3 5902 J5 NE z 39 Example Write each expression as a single quotient in which only positive exponents or radicals appear 2 Vx2l x x2l x2l 2 l l l x 3cl2 c3cl 2 x 0x l 40

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