The document discusses cube roots and their properties. It defines a cube root as the value that when multiplied by itself three times equals the original number. Cube roots are always expressed with an index of 3. Perfect cubes are numbers that can be written as the cube of another number, and their exact cube roots can be found. The document provides examples of finding cube roots of perfect cubes and simplifying cube roots by factoring the radicand into a perfect cube times another term. Not all cube roots can be simplified if the number is not a perfect cube or does not have a perfect cube factor.

1. Objectives
The student will be able to
simplify a cube root.
SOL: A.13 2009

2. The index of a cube root is
always 3.
The cube root of 64 is written as
.3
64
Cube Roots

3. What does cube root mean?
The cube root of a number is…
…the value when multiplied by itself
three times gives the original number.

4. Cube Root Vocabulary
n
x
index
radicand
radical sign

5. If a number is a perfect cube, then
you can find its exact cube root.
A perfect cube is a number that can
be written as the cube (raised to
third power) of another number.
Perfect Cubes

6. What are Perfect Cubes?
 13 = 1 x 1 x 1 = 1
 23 = 2 x 2 x 2 = 8
 33 = 3 x 3 x 3 = 27
 43 = 4 x 4 x 4 = 64
 53 = 5 x 5 x 5 = 125
 and so on and on and on…..

7. Examples:
     
3
4 4 4 4 64 
4643

because
      644444
3

because
3
64 4  

8. Examples:
3
327 
3
5
4
125
64







3
6216 
3273

5
4
125
643 
62163


9. Examples:
 33
28 aa 
 3515
464 yy 
 3412
327 mm 
aa 283 3

53 15
464 yy 
43 12
327 mm 

10. Not all numbers or expressions have
an exact cube root as in the previous
examples.
If a number is NOT a perfect
cube, then you might be able to
SIMPLIFY it.
Simplify Cube Roots

11. 2 Extract the cube root of the
factor that is a perfect cube.
1 Write the radicand as a product of
two factors, where one of the
factors is a perfect cube.
To simplify a cube root ...
3 The factors that are not perfect
cubes will remain as the radicand.

12. perfect cube
Examples:
3
227 3
23
3 36 3 2
125 4 a b ab 3 22
45 abba
3
1043
64 10 
3 36 3 23
125 4   a a b b
3
541)
3
6402)
3 7 5
500 a b3)

13. Not all cube roots
can be simplified!
• 30 is not a perfect cube.
• 30 does not have a perfect
cube factor.
Example: 3
30
cannot be simplified!
3
30