Math 1201 Date:______________________
4.2 Irrational Numbers
The value of a radical is either a rational or irrational number. Radicals that are square
roots of perfect squares, cube roots of perfect cubes, and so on, are rational numbers.
An irrational number is a number that cannot be expressed as a fraction, ๐
๐ for any
integers and ๐ and ๐. Irrational numbers have decimal expansions that neither terminate
nor repeat.
The set of irrational numbers is now added to the family of natural numbers, whole
numbers, integers, and rational numbers. The irrational numbers together with the rational
numbers form the real number system.
Real Number System
Natural Numbers โ numbers greater than zero with no decimals or fractions. These are
also called the counting numbers. {1, 2, 3, 4, 5, โฆ}
Whole Numbers โ the natural numbers combined with zero. {0, 1, 2, 3, 4, 5, โฆ}
Integers - the set of integers includes, positive numbers, zero and negative numbers
without decimals or fractions. {โฆ-3, -2, -1, 0, 1, 2, 3โฆ}
Rational Numbers - any number that can be expressed as the quotient or fraction ๐
๐ of two
integers, a numerator ๐ and a non-zero denominator ๐. Since ๐ may
be equal to 1, every integer is a rational number.
Example 1:
Sort the following numbers into rational and irrational:
1
2,4,โ6,โ9,โ17,๐,โ2
3,โ8
27
3
