Math 8 –
Name
NOTES: Square & Cube Roots
Date
Today’s Objectives
 Recognize perfect cubes.
 Find the cube root of fractions.
 Understand the relationship between cubing a number and finding the cube root of
a number.
We have been working with square roots for the past several weeks.
Since ________  ________ = 121, then
144 = ________
Two identical factors
We find cube roots in the same exact way, except we need three identical factors,
instead of two.
Since ________  ________  ________ = 8, then
3
8 = ________
Three identical factors
Example: Just as we know the first 15 perfect squares, let’s look at the first 6
perfect cubes.
3
_____ = 1
3
_____ = 4
3
_____ = 2
3
_____ = 5
3
_____ = 3
3
_____ = 6
We can find the cube root of a fraction in a way similar to how we found the square root
of a fraction.
Review: Evaluate
81
Example: Evaluate
225
3
64
216
Practice: Evaluate the following.
1.
4.
3
3
125
1
216
2.
3
5.
3
512
27
343
3.
3
6.
3
1331
8
1000
We can also solve equations that involve cube roots in a way similar to those that involve
square roots.
Review: Solve x2 = 49
Example: Solve x3 = 729
Practice: Solve the following equations.
1. Solve x3 = 125
2. Solve x3 = 2197
3. Solve x3 =
125
1000