9 CHAP - 9 SURDS AND INDICES I IMPORTANT FACTS AND FORMULAE...

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9. SURDS AND INDICES I IMPORTANT FACTS AND FORMULAE I 1. LAWS OF INDICES: (i) a m x a n = a m + n (ii) a m / a n = a m-n (iii) (a m ) n = a mn (iv) (ab) n = a n b n (v) ( a/ b ) n = ( a n / b n ) (vi) a 0 = 1 2. SURDS : Let a be a rational number and n be a positive integer such that a 1/n = n sqrt(a) is irrational. Then n sqrt(a) is called a surd of order n. 3. LAWS OF SURDS: (i) n √a = a 1/2 (ii) n √ab = n √a * n √b (iii) n √a/b = n √a / n √b (iv) ( n √a) n = a (v) m √( n √(a)) = mn √(a) (vi) ( n √a) m = n √a m I SOLVED EXAMPLES Ex. 1. Simplify : (i) (27) 2/3 (ii) (1024) -4/5 (iii)( 8 / 125 ) -4/3 Sol . (i) (27) 2/3 = (3 3 ) 2/3 = 3 ( 3 * ( 2/ 3)) = 3 2 = 9 (ii) (1024) -4/5 = (4 5 ) -4/5 = 4 { 5 * ( (-4) / 5 )} = 4 -4 = 1 / 4 4 = 1 / 256 (iii) ( 8 / 125 ) -4/3 = {(2/5) 3 } -4/3 = (2/5) { 3 * ( -4/3)} = ( 2 / 5 ) -4 = ( 5 / 2 ) 4 = 5 4 / 2 4 = 625 / 16 Ex. 2. Evaluate: (i) (.00032) 3/5 (ii)l (256) 0.16 x (16) 0.18 . Sol.
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This note was uploaded on 08/13/2011 for the course FSD 011 taught by Professor Vinh during the Spring '11 term at Beacon FL.

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9 CHAP - 9 SURDS AND INDICES I IMPORTANT FACTS AND FORMULAE...

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