What is a cube root
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the concept of a cube root. Students learn that the cube root of a number n is the value x such that x^3 = n, and that every real number—including negative numbers—has exactly one real cube root.
Key Concepts
Property The number $c$ is called a cube root of a number $b$ if $c^3 = b$. Every number has exactly one cube root. The cube root of a positive number is positive, and the cube root of a negative number is negative.
Examples The cube root of 27 is 3, written as $\sqrt[3]{27} = 3$, because $3^3 = 27$. The cube root of $ 64$ is $ 4$, written as $\sqrt[3]{ 64} = 4$, because $( 4)^3 = 64$. A cube shaped box has a volume of 1000 cubic inches. Its side length is the cube root of the volume, so $\sqrt[3]{1000} = 10$ inches.
Explanation Finding a cube root is the reverse of cubing a number (raising it to the third power).
Common Questions
What is a cube root?
The cube root of a number n is the value x such that x cubed equals n. For example, the cube root of 8 is 2 because 2^3 = 8.
How is a cube root different from a square root?
Unlike square roots, cube roots exist for negative numbers. The cube root of -8 is -2, because (-2)^3 = -8.
What is the cube root symbol?
The cube root symbol is the radical sign with a small 3: third-root(n). For example, third-root(27) = 3.
How do you calculate the cube root of a non-perfect cube?
Use a calculator or estimate between known perfect cube roots. For example, the cube root of 20 is between 2 (since 2^3 = 8) and 3 (since 3^3 = 27).
Where is what is a cube root taught?
Cube roots are introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.