Square roots and cube roots

In a nutshell

Square roots and cube roots are the inverses of the square and cube operations.

The square root of a number, $x$ , is denoted as $\sqrt{x}$ . A square root is defined as follows:

If $x=y^2$ , then $\sqrt{x}=y$ .

In other words, finding the square root of $x$ is the same thing as asking what number becomes $x$ when multiplied by itself?

Square roots can either by found by memorising square numbers, or by using a calculator.

What is the square root of $36$ ?

You should know that $6^2=6\times6=36$ . Therefore, $\underline{\sqrt{36}=6}$ .

What is the square root of $85$ ?

Use the $\sqrt{}$ button on your calculator:

$\underline{\sqrt{85}=9.219544457...}$

The cube root of a number, $x$ , is denoted as $\sqrt[3]{x}$ . A cube root is defined as follows:

If $x=y^3$ , then $\sqrt[3]{x}=y$ .

In other words, finding the cube root of $x$ is the same as asking what number, when cubed, becomes $x$ ?

Cube numbers can be very large for even smaller numbers. So, in most cases, you will have to use your calculator to find cube roots.

What is the cube root of $512$ ?

$8^3=8\times8\times8=512$ , so $\underline{\sqrt[3]{512}=8}$ .

What is the cube root of $-100$ ?

Use the $\sqrt[3]{}$ button on your calculator:

$\underline{\sqrt[3]{-100}=-4.641588834...}$