In this chapter, we will learn method to square the negative number along with solved examples.

Try understand the lesson, you should have basic understanding of the **concept of square of numbers**. Click the red link to read about the same.

## Can we square a negative number ?

Answer is **YES !!!**

You can** square any possible number** available in Math domain.

When we square a number, we basically multiply a number by itself.

So on **squaring a negative number**, we multiply the same number twice to **get the positive number**.

Consider the **below example** for better clarity.

Let’s square the number -2.

\mathtt{\Longrightarrow \ ( -2)^{2} \ }\\\ \\ \mathtt{\Longrightarrow \ -2\ \times \ -2}\\\ \\ \mathtt{\Longrightarrow \ 4} **Conclusion**

Squaring of negative number results in positive number.

### Representation of square of negative number

If (-a) is the given number, it’s square is represented as follows;

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

Hence, the whole calculation is summarized to below formula;

\mathtt{Hence,\ ( -a)^{2} =a^{2}}

### Square of negative fraction

On squaring fraction, **we multiply numerator and denominator by itself twice**.

In this case also, **the square of negative fraction results in positive fraction.**

Let (-a/b) is the given fraction.

Squaring the number, we get;

\mathtt{\Longrightarrow \ \left(\frac{-a}{b}\right)^{2} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{-a\ \times -a}{\ b\ \times \ b}}\\\ \\ \mathtt{\Longrightarrow \ \frac{a^{2}}{b^{2}}}

The above calculation is summarized by following formula;

\mathtt{\left(\frac{-a}{b}\right)^{2} =\ \frac{a^{2}}{b^{2}}}

I hope you understood the above concepts. Let us solve some problems related to this chapter.

## Squaring negative numbers – Solved examples

**(01) Square the below numbers.**

(i) -9

(ii) -0.2

(iii) -5

(iv) -2/3

(v) -6/11

(vi) -10

(vii) -2.5

(viii) -15/13

(ix) -21

(x) -30

Solution

**(i) -9**

\mathtt{\Longrightarrow \ ( -9)^{2}}\\\ \\ \mathtt{\Longrightarrow \ -9\ \times \ -9}\\\ \\ \mathtt{\Longrightarrow \ 81} **Hence, 81 is the solution**

**(ii) -0.2**

\mathtt{\Longrightarrow \ ( -0.2)^{2}}\\\ \\ \mathtt{\Longrightarrow \ -0.2\ \times \ -0.2}\\\ \\ \mathtt{\Longrightarrow \ \frac{-2}{10} \times \frac{-2}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{100}}\\\ \\ \mathtt{\Longrightarrow \ 0.04}

Hence, **0.04 is the solution.**

**(iii) -5**

\mathtt{\Longrightarrow \ ( -5)^{2}}\\\ \\ \mathtt{\Longrightarrow \ -5\ \times \ -5}\\\ \\ \mathtt{\Longrightarrow \ 25}

Hence, **25 is the solution**.

**(iv) -2/3**

\mathtt{\Longrightarrow \ \left(\frac{-2}{3}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-2}{3} \times \frac{-2}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{9}}

Hence, **4/9 is the final solution.**

**(v) -6/11**

\mathtt{\Longrightarrow \ \left(\frac{-6}{11}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-6}{11} \times \frac{-6}{11}}\\\ \\ \mathtt{\Longrightarrow \ \frac{36}{121}}

Hence, **36/121 is the solution.**

**(vi) -10**

\mathtt{\Longrightarrow \ ( -10)^{2}}\\\ \\ \mathtt{\Longrightarrow \ -10\ \times \ -10}\\\ \\ \mathtt{\Longrightarrow \ 100}

Hence, **100 is the solution.**

**(vii) -2.5**

\mathtt{\Longrightarrow \ ( -2.5)^{2}}\\\ \\ \mathtt{\Longrightarrow \ -2.5\ \times \ -2.5}\\\ \\ \mathtt{\Longrightarrow \ \frac{-25}{10} \times \frac{-25}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{625}{100}}\\\ \\ \mathtt{\Longrightarrow \ 6.25}

Hence, **6.25 is the final solution.**

**(viii) -15/13**

\mathtt{\Longrightarrow \ \left(\frac{-15}{13}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-15}{13} \times \frac{-15}{13}}\\\ \\ \mathtt{\Longrightarrow \ \frac{225}{169}}

Hence, **225/169 is the solution.**

**(ix) -21**

\mathtt{\Longrightarrow \ ( -21)^{2}}\\\ \\ \mathtt{\Longrightarrow \ -21\ \times \ -21}\\\ \\ \mathtt{\Longrightarrow \ 441}

Hence, **441 is the solution**.

**(x) -30**

\mathtt{\Longrightarrow \ ( -30)^{2}}\\\ \\ \mathtt{\Longrightarrow \ -30\ \times \ -30}\\\ \\ \mathtt{\Longrightarrow \ 900}

Hence, **900 is the solution**.