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Concept

Cube Root

The cube root of a number

a

is a number that, when multiplied by itself three times, equals

a .

For example,

2

is the cube root of

8 .

2 \cdot 2 \cdot 2 = 8 \Rightarrow 38 = 2

Cube roots and raising a number to the third power are operations that undo each other.

$3 a^{3} = a and (3 a)^{3} = a$

Unlike square roots, cube roots can yield negative results. This is because the product of three negative factors is negative.

(- 2) (- 2) (- 2) = - 8 \Rightarrow 3 - 8 = - 2

Extra

Cube Root of Fractions and Decimal Numbers

Separate from the integers, the cube roots of fractions can be calculated by taking cube roots of the numerator and denominator separately. Consider the following example.

\frac{8}{1 2 5} = \frac{2 ^{3}}{5 ^{3}} \Rightarrow 3 \frac{8}{1 2 5} = \frac{2}{5}

The cube roots of decimal numbers can be calculated by writing them in the fraction form, calculating the cube roots of the numerator and denominator separately. Consider the following example.

0.027 = \frac{2 7}{1 0 0 0} = \frac{3 ^{3}}{1 0 ^{3}} ⇓ 3 \frac{2 7}{1 0 0 0} = \frac{3}{1 0} = 0.3

Exercises

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