Surd
An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational...
An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational...Rational and Irrational Numbers Introduction
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1h..
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1h..Irrational numbers 1 Animation
Rational and Irrational Numbers..
Rational and Irrational Numbers..Irrational numbers 2 Animation
Rational and Irrational Numbers..
Rational and Irrational Numbers..Suggested answer:
a) Reciprocal ratio of 3:5 b) Duplicate ratio of 2:3 =2 2 :3 2 =4:9 c) Triplicate ratio of 3:4 = 3 3 :4 3 = 27:64 d) Sub duplicate ratio of 25:16 =5:4 e) Sub triplicate ratio of 27:8 = 3:2..
a) Reciprocal ratio of 3:5 b) Duplicate ratio of 2:3 =2 2 :3 2 =4:9 c) Triplicate ratio of 3:4 = 3 3 :4 3 = 27:64 d) Sub duplicate ratio of 25:16 =5:4 e) Sub triplicate ratio of 27:8 = 3:2..Illustrative Examples
1. Find the compounded ratio of a) 5:14 and 7:15 b) a+b:a-b; (a 2 -b 2 ):(a 2 +b 2 ) and a 2 +b 2 :(a+b) 2 . 2. In the ratio 7:8, if the consequent is 40, what is the antecedent? 3...
Indices
We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 Here 2 is called the base and 6 is called the power (or index or exponent). We say that "64 is equal to base 2 raised to the power 6". The Laws of Indices a..
Conjugate surds
Conjugate surds - is the conjugate surd of . Their product is a rational number, In the above example (6), and are conjugate surds of each other..
Conjugate surds - is the conjugate surd of . Their product is a rational number, In the above example (6), and are conjugate surds of each other..Proof:
We must prove two statements. If x A and x B then, by the statement "two sets A and B are different if there exists an element which belongs to one set but not to the other" and by hypothesis, A = B is contradicted. Thus A B. Similarly B ..
We must prove two statements. If x A and x B then, by the statement "two sets A and B are different if there exists an element which belongs to one set but not to the other" and by hypothesis, A = B is contradicted. Thus A B. Similarly B .. Result
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