lesson 1

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Real Numbers & Radicals

Basic Algebra & Polynomials

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jdsmathnotes

UNIT 1 : ALGEBRA PREP

LESSON 1: REAL NUMBERS & RADICALS

$Text Box: The Number Systems Defined: Natural Numbers – the ordinary counting numbers. N = {1, 2, 3, 4, 5, 6, . . . } Whole Numbers – the natural numbers including the zero element. W = {0, 1, 2, 3, 4, 5, 6, . . . } Integers – the natural numbers including their negatives and zero. I = { . . . –4, -3, -2, -1, 0, 1, 2, 3, . . .} Rational Numbers - the set of all possible ratios of integers with non-zero denominators. Basically this includes all fractions (positive and negative) in the form a/b as the definintion below suggests. In decimal form this would include all terminating decimals and non-terminating, repeating decimals which can be obtained from dividing out the fraction form of the rational number. Irrational Numbers – these are numbers that are not rational – ie the set of all non – terminating, non – repeating decimals. Real Numbers – the union of the rational numbers and irrational numbers is the Real number system.$

Note: In these notes, we are talking about real numbers unless otherwise stated.

Intervals:

The interval can also be illustrated on a number line as below.

OR

NOTE: Open circles or round brackets indicate that the end point indicated is not included.

The interval can also be illustrated on a number line as below.

NOTE: Closed circles or square brackets indicate that the end point indicated is included.

REAL NUMBERS - RADICALS

Examples Of Radicals:

NOTE: Each of these examples is an irrational real number.

Properties of Radicals:

Text Box:

Example 1:

Mixed and Entire Radicals:

Text Box: Tips for Changing to Mixed Radicals:
· Break the radical into two factors
· Use the following set of perfect squares to get the first factor
· {4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, …}
· Take the square root of the first number to get the first factor of the mixed radical.