Name: ____________________________________________________
Cubes and Cube Roots: Note sheet
How to Cube a Number:
3
Example: What is 3 cubed?
= 3 x 3 x 3 = 27
3
3
3
Note: We write 3 cubed as 33
Some More Cubes:
1.) 4 cubed = 43 = ____ x ____ x ____ =
2.) 5 cubed = 53 = ____ x ____ x ____ =
Cube Roots
A cube root goes the other direction: (Now you are asking yourself what number can I multiply together
three times to get the solution).
Ex: 3 cubed is 27, so the CUBE ROOT of 27 is 3 (Why? Because 3x3x3 equals 27)
Examples:
1.) What is the cube root of 64? (hint: what number can I multiply together three times to get 64?) ____
2.) What is the cube root of 125? _______
3.) What is the cube root of 216? ______
The Cube Root Symbol
3
√ This is the special symbol that means “cube root”, it is the radical symbol (also used for square
roots) with a little three to mean cube root.
𝟑
*You can use it like this: √𝟐𝟕 = 3 (You would say “The cube root of 27 equals 3)
Perfect Cubes:
-The cube of the whole numbers:
Perfect
Cubes:
1
2
3
4
5
6
7
8
9
10
1
8
27
64
125
216
343
512
729
1000
It is easy to work out the cube root of a perfect cube, but it is REALLY HARD to work out other cube
roots.
Example: What is the cube root of 30?
1. If you know what perfect cube roots are around the number that will help you narrow your search.
So what perfect cube is close to 30? 27-which has a root of 3 so you know you should start with
numbers bigger than three. (You know it’s not 4 because 4x4x4=64)
2. Use guess and check to see how close you can get to 30. (You can use a calculator for the
multiplication).



Let’s try 3.5: 3.5x3.5x3.5=42.875
Let’s try 3.2: 3.2x3.2x3.2=32.768
Let’s try 3.1: 3.1x3.1x3.1=29.791
As you can see we can’t find the EXACT cube root of 30, we are only finding an approximation or
estimation.
Now you try to work out NOT perfect cube roots: (Remember it’s your best estimation).
3
1.) √89
3
2.) √102
*If you want more information, there is a video at the following link that can help explain cube roots to
you.
http://www.youtube.com/watch?v=4hKlBV3VC4Y
Cubes and Cube Roots Worksheet
Name: ________________________________________ Date: ___________________
1. What does it mean to “cube” a number?
2. Let’s practice, complete the following cubes.
a.) 13 =
b.) 23 =
c.) 33 =
d.) 63 =
e.) 83 =
f.) 103 =
The inverse of cubing a number is……
3
3.) √8 =
3
5.) √125=
3
9.) √102 =
4.) √512=
3
3
6.) √64=
Now, estimate the cube root of the following:
3
7.) √30=
8.) √48=
3