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Workbook

We can not solve x  2 2 0 on because there is no number whose square is 2 in the set of
rational numbers. In fact,

x  2 0  x  2  x   2
2
2
a
We can not write 2 as , ,a b , b 
0
b

a
Irrational Numbers: A number that can not be expressed as called irrational number. It is denoted
b
by . An example of an irrational number is 2 . For example

2 1,41421356237... Also,   3,1415926... 7  2,645751...
The digits never repeat
and never stop.

Real Numbers: So far, we have talked about rational numbers (including integers) and irrational
numbers. All of these numbers combined are called the real numbers. The relationship among the sets
of numbers discussed thus far are illustrated in the figure below.

Real Numbers

Rational Numbers Irrational Numbers

Integer Numbers
Natural Numbers

Counting Numbers

Real Number Line and Coordinate Plane

Every real number corresponds to a point on a number line. For this reason, we sometimes call the
number line the real number line.

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