Question

what is cube and cube root
explain with a concept
give me answer​

Answer 1

$\large\underline{\large\underline{\text{Explanation}}}$

The cube of a number is itself multiplied three times. The cube root is the opposite. It finds the cubed number.

Let's take an example.

The cube if 2 is,

$\cdots\longrightarrow2^{3}=8.$

The cube root of $8$ is,

$\cdots\longrightarrow\sqrt[3]{8}=2.$

We can also relate this to the volume and the side of a solid cube.

e.g.) If the side length is 2, the volume is 8.

e.g.) If the volume is 8, the side is 2.

In algebra, we write the cube of $x$ as $x^{3}$.

Then as an extent of the law of exponents $(a^{r})^{s}=a^{rs}$, $x^{\frac{1}{3}}$ is taken as a cube root, or we write it as $\sqrt[3]{x}$.

Let us find the cube root of the cube.

$\cdots\longrightarrow(x^{3})^{\frac{1}{3}}=x^{\frac{3}{3}}=x.$

And let us find the cube of the cube root.

$\cdots\longrightarrow(x^{\frac{1}{3}})^{3}=x^{\frac{3}{3}}=x.$

Since the composition of two functions brings the old number, they are called the inverse function.