Pre-Algebra Chapter 9

A Follow-Up of Lesson 9-5
Graphing Irrational Numbers
In Lesson 2-1, you learned to graph integers on a number line. Irrational numbers
can also be graphed on a number line. Consider the irrational number 53. To
graph 53, construct a right triangle whose hypotenuse measures 53 units.
Step 1 Find two numbers whose squares have a sum of 53. Since 53 49 4
or 7 2 2 2 , one pair that will work is 7 and 2. These numbers will be the
lengths of the legs of the right triangle.
Step 2
Draw the right triangle
• First, draw a number line on grid paper.
01 2345678
• Next, draw a right
triangle whose legs
measure 7 units and
2 units. Notice that
this triangle can be
drawn in two ways.
Either way is correct.
0 1 2 3 4 5 678
2 units
7 units
0 1 2 3 4 5 678
Step 3
Graph 53 .
• Open your compass
to the length of the
hypotenuse.
• With the tip of the
compass at 0, draw
an arc that intersects
the number line
at point B.
0 1 2 3 4 5 678
0
• The distance from 0 to B is 53 units. From the graph, 53 7.3.
1 2 3 4 5 6
B
7 8
Model and Analyze
Use a compass and grid paper to graph each irrational number on a
number line.
1. 5 2. 20 3. 45 4. 97
5. Describe two different ways to graph 34.
6. Explain how the graph of 2 can be used to locate the graph of 3.
Investigating Slope-Intercept Form 465
Algebra Activity Graphing Irrational Numbers 465