### Theory:

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

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 $$\sqrt{a}$$ or $$a^{\frac{1}{3}}$$.
Example:
Find the cube root of $$64$$.

Solution:

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

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