### Theory:

Square and Square numbers:

In our earlier classes, we learned about power and exponent. When the exponent of a natural number is $$2$$, the number has to be multiplied by itself which is called as square, and the obtained number is called a square number or a perfect square.

Square:
When the exponent of a natural number is $$2$$, the number has to be multiplied by itself, and this is called square.

For example: ${3}^{2}$, ${6}^{2}$, ${11}^{2}$, ${14}^{2}$.

Square number:

We know that the area of the square is $a×a$. That is multiplying the side by itself we get the area of the square.

Similar to this concept square of a number is obtained by multiplying it by itself.

That is if $a×a=b$. Therefore ${a}^{2}=b$ this is also true. Then we can say that the number $$b$$ is the square of number $$a$$.

For example:

$\begin{array}{l}{3}^{2}=3×3=9\\ \\ {6}^{2}=6×\phantom{\rule{0.147em}{0ex}}6=36\\ \\ {11}^{2}=11×\phantom{\rule{0.147em}{0ex}}11=11\\ \\ {14}^{2}=14×14=196\end{array}$

Now the following table consists of squares of first $$20$$ numbers. Students are advised to memorize it.

 Number Square Number Square number 1 ${1}^{2}$ $$= 1 × 1 = 1$$ 11 ${11}^{2}$ $$= 11 × 11 = 121$$ 2 ${2}^{2}$ $$= 2 × 2 = 4$$ 12 ${12}^{2}$ $$= 12 × 12 = 144$$ 3 ${3}^{2}$ $$= 3 × 3 = 9$$ 13 ${13}^{2}$ $$= 13 × 13 = 169$$ 4 ${4}^{2}$ $$= 4 × 4 = 16$$ 14 ${14}^{2}$ $$= 14 × 14 = 196$$ 5 ${5}^{2}$ $$= 5 × 5 = 25$$ 15 ${15}^{2}$ $$= 15 × 15 = 225$$ 6 ${6}^{2}$ $$= 6 × 6 = 36$$ 16 ${16}^{2}$ $$= 16 × 16 = 256$$ 7 ${7}^{2}$ $$= 7 × 7 = 49$$ 17 ${17}^{2}$ $$= 17 × 17 = 289$$ 8 ${8}^{2}$ $$= 8 × 8 = 64$$ 18 ${18}^{2}$ $$= 18 × 18 = 324$$ 9 ${9}^{2}$ $$= 9 × 9 = 81$$ 19 ${19}^{2}$ $$= 19 × 19 = 361$$ 10 ${10}^{2}$ $$= 10 × 10 = 100$$ 20 ${20}^{2}$ $$= 20 × 20 = 400$$