What is a Cube Root?
A cube root of a number a is a value b such that b³ = a, written as ∛a. For example, ∛27 = 3 because 3³ = 27, and ∛−8 = −2 because (−2)³ = −8. Unlike square roots, cube roots can be negative because a negative number cubed stays negative. Finding cube roots reverses the cubing operation and is a key skill in Grade 8 math from enVision Mathematics Chapter 1: Real Numbers, where students learn to work with perfect cubes and estimate non-perfect cube roots on a number line.
Key Concepts
A cube root of a number $a$ is a number $b$ such that $b^3 = a$. The cube root is denoted by the symbol $\sqrt[3]{a}$.
$$ \text{If } b^3 = a, \text{ then } \sqrt[3]{a} = b $$.
Common Questions
What is a cube root?
A cube root of a number is a value that, when multiplied by itself three times, gives the original number. The cube root of 64 is 4 because 4 × 4 × 4 = 64. It is written with the radical symbol ∛.
How do you find the cube root of a number?
For perfect cubes, identify which integer cubed gives the number: ∛125 = 5 because 5³ = 125. For non-perfect cubes, estimate by finding the two consecutive integers whose cubes bracket the number, then refine with a calculator.
Can cube roots be negative?
Yes. Since a negative number multiplied by itself three times remains negative, cube roots of negative numbers are negative. For example, ∛(−27) = −3 because (−3)³ = −27. This differs from square roots, which cannot be negative in real numbers.
What are the first ten perfect cubes?
The first ten perfect cubes are: 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000. Memorizing these helps you quickly identify cube roots in Grade 8 math problems.
How are cube roots different from square roots?
Square roots undo squaring (x²) while cube roots undo cubing (x³). Square roots of negative numbers are not real, but cube roots of negative numbers are real and negative. Every real number has exactly one real cube root.
When do students learn about cube roots?
Cube roots are typically introduced in Grade 8 as part of the real numbers unit. In enVision Mathematics Grade 8, this concept appears in Chapter 1 alongside square roots and irrational numbers.