### Theory:

We are well aware of doing the arithmetic operation like addition and subtraction, and we can use these operations to calculate the square of the number in a simple way.

In your earlier classes, you could have studied about the formula of ${\left(a+b\right)}^{2}$, That is ${\left(a+b\right)}^{2}={a}^{2}+\mathit{2ab}+{b}^{2}$.

Similarly ${\left(a-b\right)}^{2}={a}^{2}-\mathit{2ab}+{b}^{2}$

We can use the above two formulas to calculate the square of a number.

Let's see an example to understand this method clearly.

i) Calculate the square of 16.

We have to find the square of 16. That is ${16}^{2}$

We can rewrite  ${16}^{2}$ as ${\left(15+1\right)}^{2}$, ${\left(14+2\right)}^{2}$, ${\left(13+3\right)}^{2}$ and so on.

That is  ${\left(15+1\right)}^{2}$ $$=$$ ${\left(14+2\right)}^{2}$ $$=$$  ${\left(13+3\right)}^{2}$ $$=$$ ${16}^{2}$

To avoid complexity, we take ${\left(15+1\right)}^{2}$ $$=$$ ${16}^{2}$.

Let $$a =$$ 15 and $$b = 1$$.

Now we substitute the values of $$a$$ and $$b$$ in ${\left(a+b\right)}^{2}$.

$\begin{array}{l}{\left(a+b\right)}^{2}={a}^{2}+\mathit{2ab}+{b}^{2}\\ \\ {\left(15+1\right)}^{2}={15}^{2}+\mathit{2}\left(15×1\right)+{1}^{2}\\ \\ {\left(15+1\right)}^{2}=225+2\left(15\right)+1\\ \\ {\left(16\right)}^{2}=225+30+1\\ \\ 256=256\end{array}$

Let's see another example using ${\left(a-b\right)}^{2}={a}^{2}-\mathit{2ab}+{b}^{2}$ formula.

II) Calculate the square of 26.

We have to find the square of 26. That is ${26}^{2}$

We can rewrite  ${26}^{2}$ as ${\left(27-1\right)}^{2}$, ${\left(28-2\right)}^{2}$, ${\left(29-3\right)}^{2}$ and so on.

That is  ${\left(27-1\right)}^{2}$ $$=$$ ${\left(28-2\right)}^{2}$ $$=$$  ${\left(29-3\right)}^{2}$ $$=$$ ${26}^{2}$.

To avoid complexity, we take ${\left(27-1\right)}^{2}$ $$=$$ ${26}^{2}$.

Let $$a =$$ 27 and $$b = 1$$.

$\begin{array}{l}{\left(a-b\right)}^{2}={a}^{2}-\mathit{2ab}+{b}^{2}\\ \\ {\left(27-1\right)}^{2}={27}^{2}-\mathit{2}\left(27×1\right)+{1}^{2}\\ \\ {\left(15-1\right)}^{2}=729-2\left(27\right)+1\\ \\ {\left(26\right)}^{2}=729-54+1\\ \\ 676=676\end{array}$

Generally, we multiply the number by itself to find the square of the number, but if the number consists more than three digits like ($$888, 999, 1000, 1500$$), then we can prefer this method to find the square of the number easily.