Chapter V Characteristics of quadratic number and square root form and it uses in solving simple problem

(1. Characteristics of quadratic number) A. Quadratic rational number on integer Rational number is which can be notated by, with a and b are integers and b ≠ 0. B. Definition of quadratic rational number of positive integer If a is a rational number and n is positive integer therefore repeated multiplication of n factor of a is Written as a n C. Characteristic of quadratic rational number of positive integer 1.Characteristics of multiplication of quadratic number Character: If a is rational number and m, n are positive integer therefore a m × a n = a m+n 2.Characteristic of division of quadratic number If a is rational number, a ≠ 0, and m, n are positive integer, therefore With m > n.

3.Characteristic of power of quadratic number Character : If a is rational number and m, n are positive integer therefore (a m ) n = a m×n = a n×m 4. Characteristic of power of multiplication form character: If n is positive integer and a, b are rational number therefore (a × b) n = a n × b n 5.Characteristics of power of division form Character : If a, b are rational numbers, b ≠ 0, and n is positive integer, therefore 6.Characteristic of sum and subtraction of quadratic number Character: If a, p, q are rational numbers and m, n are positive integers, with m ≥ n therefore pa n + qa m = a n (p + qa m–n )

A sequence U 1, U 2, U 3,..., U n, U n + 1 are called arithmetic sequence If for each n integers which available for U n + 1 – U n = U n – U n–1 =... = U 2 – U 1 = b. D. Characteristics of quadratic rational of negative integer and zero a.Definition of quadrate of negative integer Definition : If a is rational number, a ≠ 0, and n is positive integer, therefore a –n = b.Definition of zero quadrate Definition : a 0 = 1, with a is rational number and a ≠ 0

(2. Form of square root and fraction quadrate) A. Real number B. Definition of square root Defenisi : C. Simplifying square root Character: With a and b are positive rational number. Real number is combination of set of rational number and set of irrational. D. Operation of algebra on square root a.Sum and subtraction on square root character:

E. Rationalize denominator of fraction b.Multiplication on square root F. Fraction quadrate With a, b, c, d are rational numbers, b ≥ 0, and d ≥ 0. c.Division on square root form character: or With a and b are rational numbers, a ≥ 0, and b > 0. e.g. :Solving: e.g. : solving: