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.**