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Name: ______________________
Class: __________________
M8-U7: Notes #3 – Irrational Square and Cube Roots
Date: __________________
WARM-UP: List perfect squares & perfect cubes
Mr. Freeman’s farm has a square cornfield. It has an area of 50 square yards. What is the length
of the cornfield?
Example 1:
Solve the following equations:
2
1. x  10
2. x 3  10
Try it: Solve the equation:
a. x 2  20
b. x 3  50
1
3. x 3  30
Numbers with non-terminating and non-repeating decimal representations are called
irrational numbers. They cannot be expressed as ratios of integers; can’t be written as
fractions.
The number 10 is an irrational number. You had trouble finding an exact terminating or
repeating decimal representation for 10 because such a representation does not exist. Other
irrational numbers are
2 , and
3 , and
5 . In fact,
of n that is not a perfect square number. Also
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n is an irrational number for any value
n is also irrational for any value of n that is not a
perfect cube.
Since these roots are irrational, the only decimal representation possible is an approximation.
2 Methods to Approximate Irrational Square Roots:
Guess & Check:
1. Determine which two whole numbers the square root must be between.
2. Choose a number between the two whole numbers.
3. Multiply your guess by itself (square it).
4. Was your guess too low or too high?
5. Make another guess, and repeat.
Repeated division:
1. Determine which two whole numbers the square root must be between.
2. Choose a number between the two whole numbers.
3. Divide the square by your choice (the divisor).
4. Choose a number between the divisor and the quotient, and repeat.
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Example C: Estimating the Value of a Square Root and Place it on a Number Line:
Without using the square root key on your calculator, approximate the value of
two decimal places. Plot the square root on the number line and label it.
a.
70
b.
35
a.
28
b.
 38
Try It!
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n to
Practice: identify the following as rational or irrational.
1.

2.
2
9
3.
14
99
4.
 121
5.
16
6.
0.25
7.
2
MULTIPLE CHOICE:
8.
Which number on this list is rational?
12, 14, 0.76, 
A.
C.
9.
11.
B.
D.

14
Which number on this list is rational?
 5 , 25, 75, 18
A.
C.
10.
12
0.76
 5
75
25
18
B.
D.
Which number on this list is irrational?
9
 0.88, 2 , 36, 40
11
A.
 0.88
B.
C.
36
D.
2
9
11
40
When is a number irrational?
A.
B.
C.
D.
When it can be written as a simple fraction.
When it cannot be written as a simple fraction.
When a decimal is repeating.
When a decimal is terminating.
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