# Square of negative number

In this chapter, we will learn to find the value of square of negative number with examples.

If you want to review the basics of square of numbers, click the red link.

## Square of negative number

The square of negative number is found by multiplying the same number twice by itself.

Note that the square of negative number is always a positive number.

The general form of square of negative number is given as;

\mathtt{( -m)^{2} \Longrightarrow \ ( -m) \times \ ( -m)}\\\ \\ \mathtt{( -m)^{2} \Longrightarrow \ ( m)^{2}}

### Why square of negative number is positive ?

This is because multiplication of two negative sign results in positive sign.

While squaring negative number, we multiply same negative number twice which generate positive number.

## Examples of Square of negative number

Given below are some examples of square of negative number for your understanding.

Example 01
Find the square of – 25

Solution
To get the square, multiply the number by itself.

\mathtt{\Longrightarrow ( -25)^{2}}\\\ \\ \mathtt{\Longrightarrow \ ( -25) \times \ ( -25)}\\\ \\ \mathtt{\Longrightarrow \ 625}

Hence, 625 is the square of – 25.

Example 02
Find the square of -31

Solution
Multiply the number by itself.

\mathtt{\Longrightarrow ( -31)^{2}}\\\ \\ \mathtt{\Longrightarrow \ ( -31) \times \ ( -31)}\\\ \\ \mathtt{\Longrightarrow \ 961}

Hence, 961 is the square of -31.

Example 03
Find the square of -90

Solution
Multiply the number by itself.

\mathtt{\Longrightarrow ( -90)^{2}}\\\ \\ \mathtt{\Longrightarrow \ ( -90) \times \ ( -90)}\\\ \\ \mathtt{\Longrightarrow \ 8100}

Hence, 8100 is the square of -90

Example 04
Find the square of -101

Solution
Multiply the number by itself

\mathtt{\Longrightarrow ( -101)^{2}}\\\ \\ \mathtt{\Longrightarrow \ ( -101) \times \ ( -101)}\\\ \\ \mathtt{\Longrightarrow \ 10201}

Hence, 10201 is the square of -101.

Example 05
Find the square of -24

Solution
Multiply the number by itself.

\mathtt{\Longrightarrow ( -24)^{2}}\\\ \\ \mathtt{\Longrightarrow \ ( -24) \times \ ( -24)}\\\ \\ \mathtt{\Longrightarrow \ 576}

Hence, 576 is the square of -24.