Maths Essay

570 WordsAug 11, 20153 Pages
INDICES, SURDS & LOGARITHMS Indices For any real number a ( (, and n is a positive integer, so [pic] , n times is call as ‘ a the power of n’, which a is the base and n is the index or exponent. For example: [pic] [pic] Law of Indices a) [pic] b) [pic] c) [pic] d) [pic] e) [pic] Zero Index [pic] [pic] Negative Index [pic] Fractional Index [pic] Example: | | | |1. [pic] |4. [pic] | |[pic] |5. [pic] | |2. [pic] |6. [pic] | |[pic] |8. [pic] | |3. [pic] | | |7. [pic] | | Exercise: 1. Simplify the following expressions. a) [pic] b) [pic] c) [pic] d) [pic] e) [pic] 2. If [pic], prove that [pic] 3. Solve the following equations. a) [pic] b) [pic] c) [pic] d) [pic] Surds A surd is an irrational number of the form [pic] , where ‘n’ is a positive integer and ‘a’ is a real number which is not a perfect square. For example, [pic] and [pic] are surd but [pic] is not a surd since [pic]. The following

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