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The inverse operation of a cube is cube root. The symbol used to represent the cube root is $$\sqrt[3]{}$$.

A cube root is a unique value that gives us the original number when we multiply itself by three times.

The cube root of $$a$$ is denoted by $$\sqrt[3]{a}$$ or $$a^{\frac{1}{3}}$$.
Example:
Find the cube root of $$64$$.

Solution:

$$\sqrt[3]{64} = \sqrt[3]{4 \times 4 \times 4}$$ $$= \sqrt[3]{4^3}$$ $$= 4$$

Thereforethe cube root of $$64$$ is $$4$$.
By the observation of the above example, we can conclude that:

The cube of $$4$$ is $$64$$.

The cube root of $$64$$ is $$4$$.

The following table consist of cube and cube roots of the first $$20$$ numbers.

 Number Cube number Cube root Number Cube number Cube root 1 $$1^3 = 1$$ $$\sqrt[3]{1} = 1$$ 11 $$11^3 = 1331$$ $$\sqrt[3]{1331} = 11$$ 2 $$2^3 = 8$$ $$\sqrt[3]{8} = 2$$ 12 $$12^3 = 1728$$ $$\sqrt[3]{1728} = 12$$ 3 $$3^3 = 27$$ $$\sqrt[3]{27} = 3$$ 13 $$13^3 = 2197$$ $$\sqrt[3]{2197} = 13$$ 4 $$4^3 = 64$$ $$\sqrt[3]{64} = 4$$ 14 $$14^3 = 2744$$ $$\sqrt[3]{2744} = 14$$ 5 $$5^3 = 125$$ $$\sqrt[3]{125} = 5$$ 15 $$15^3 = 3375$$ $$\sqrt[3]{3375} = 15$$ 6 $$6^3 = 216$$ $$\sqrt[3]{216} = 6$$ 16 $$16^3 = 4096$$ $$\sqrt[3]{4096} = 16$$ 7 $$7^3 = 343$$ $$\sqrt[3]{343} = 7$$ 17 $$17^3 = 4913$$ $$\sqrt[3]{4913} = 17$$ 8 $$8^3 = 512$$ $$\sqrt[3]{512} = 8$$ 18 $$18^3 = 5832$$ $$\sqrt[3]{5832} = 18$$ 9 $$9^3 = 729$$ $$\sqrt[3]{729} = 9$$ 19 $$19^3 = 6859$$ $$\sqrt[3]{6859} = 19$$ 10 $$10^3 = 1000$$ $$\sqrt[3]{1000} = 10$$ 20 $$20^3 = 8000$$ $$\sqrt[3]{8000} = 20$$