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More Lessons For Grade 8
Perfect Squares
Math Worksheets
In these lessons, we will learn what are perfect cubes and how to calculate the cube root of a perfect cube.
A cube is a number multiplied by itself three times:
a3 = a × a × a
Examples:
23 = 2 × 2 × 2 = 8
(-3)3 = -3 × -3 × -3 = -27
Finding the cube root is the inverse operation of cubing.
The cube root of a number a is a value x such that:
x3 = a
It is written as ∛a = x
Cube root works for all real numbers (positive, negative, or zero).
∛ is the special symbol that means “cube root”. It is the radical symbol √ with a little
three to mean cube root.
You can use it like this:
∛27 = 3.
Examples:
∛8 = 2 (since 33 = 8)
∛(-27) = -3 (since (-3)3 = 27
∛0 = 0
A perfect cube is an integer that is the cube of another integer:
n = k33 (where k is an integer)
For example, 125 is a perfect cube since 125 = 5 × 5 × 5 = 53
Some other examples of perfect cubes are 1, 8, 27, 64, 125, 216, 343, …
The following table shows perfect cubes from 1 to 1000 and their corresponding cube roots. Scroll down the page for more examples of how to evaluate cube root of perfect cubes.
It is easy to work out the cube root of a perfect cube, but it is hard to work out other cube roots.
Exponent Worksheets
Practice your skills with the following exponent worksheets:
Printable & Online Exponent Worksheets
How to Find Cube Roots
Method 1: Memorization (for Small Numbers)
Memorize cubes of integers 1–10 (see table above).
Method 2: Prime Factorization
Example: Find ∛216
Example:
What is the smallest positive whole number that is a perfect cube and is a multiple of 24?
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