The cube of a number equals multiplying the number by itself three times. Positive numbers yield positive cubes, negative numbers yield negative cubes, and zero cubed is zero.
⚠Note: Cube operations amplify values. Large numbers may exceed normal display range and results will be shown in scientific notation.
What is a Cube?
A cube is the third power operation in mathematics, denoted by x³. It represents multiplying a number by itself three times, equivalent to calculating the volume of a cube.
Volume Concept
A cube with side length x has volume V = x³. This is the origin of the term "cube" for the third power.
Squares are the second power (x² = x × x), cubes are the third power (x³ = x × x × x). Squares calculate area, cubes calculate volume. Cubes grow faster than squares.
Why is the cube of a negative number negative?▼
Because a cube is three consecutive multiplications. (-2)³ = (-2)×(-2)×(-2) = 4×(-2) = -8. An odd number of negative factors yields a negative result, so odd powers preserve the original sign.
Can decimals and fractions be cubed?▼
Yes. Cubes apply to all real numbers. For example, (0.5)³ = 0.125, and (1/2)³ = 1/8 = 0.125. Fractional cubes can produce very small numbers.
What is the relationship between cube and cube root?▼
The cube root is the inverse of cube. If x³ = a, then x = ∛a. For example, ∛8 = 2 because 2³ = 8. Every real number has exactly one real cube root.
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