overview

In this page, cube of a number and cube root of a number are revised.

cube

${5}^{3}=5\times 5\times 5=125$?

An exponent of power $3$ is called *cube* of the number.

eg: Cube of $7$ is ${7}^{3}=343$.

The word "cube" means : the 3D shape of equal sides and $90}^{\circ$ angles" between edges. The exponent cube is representative of "volume of the shape cube, side to the power 3".

cube root

${8}^{\frac{1}{3}}={(2\times 2\times 2)}^{\frac{1}{3}}=2$

$\sqrt[3]{8}=\sqrt[3]{2\times 2\times 2}=2$

An exponent of power $\frac{1}{3}$ or the $3$rd root is called *cube root* of the number.

eg: Cube root of $64$ is ${64}^{\frac{1}{3}}=\sqrt[3]{64}=4$.

examples

Cube of $3$ is $3}^{3$.

Cube root of $8$ is $\sqrt[3]{8}={8}^{\frac{1}{3}}$.

finding cube root

How to find $\sqrt[3]{216}$?

Cube root is a form of roots. In roots, we learned to perform prime factorization to find the root.

$\sqrt[3]{216}$

$=\sqrt[3]{2\times 2\times 2\times 3\times 3\times 3}$

$=2\times 3$

$=6$

summary

**Cube of a number** : A number to the power $3$ is the cube of the number.

eg: ${6}^{3}=6\times 6\times 6=216$

**Cube Root of a number** : A number to the power $\frac{1}{3}$ is the cube root of the number.

eg: $\sqrt[3]{216}=6$ as ${6}^{3}=216$.

**Finding Cube Roots** : To find cube root of a number, express the number in prime factors and group the factors.

eg: $\sqrt[3]{1000}$ $=\sqrt[3]{2\times 2\times 2\times 5\times 5\times 5}$ $=2\times 5=10$

Note: This method is suitable for finding cube roots resulting in integers.

Outline

The outline of material to learn "Exponents" is as follows.
Note: * click here for detailed outline of Exponents s *

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