### Theory:

We know that the inverse (opposite) operation of addition is subtraction and the inverse operation of multiplication is division.

Similarly, finding the square root is the inverse operation of squaring.

That is, the square root is the inverse operation of a square.
The square root of a number is represented by the symbol of $\sqrt{}$.

The square root of a number $$n$$ can be written as $$\sqrt{n}$$ (or) ${n}^{\frac{1}{2}}$.
Example:
1. The square of $$2$$ is $$4$$. That is $$2^2 = 4$$.

The square root (inverse) of $$4$$ is $$2$$. That is $$\sqrt{4} = 2$$.

2. The square of $$5$$ is $$25$$. That is $$5^2 = 25$$.

The square root (inverse) of $$25$$ is $$5$$. That is $$\sqrt{25} = 5$$.
Positive root and Negative root
If we square the negative number, we get the positive number as a product.

${\left(-1\right)}^{2}=\left(-1\right)×\left(-1\right)=1$, because  $$(-) \times (-) = +$$

(i) $$(-2)^2 = (-2) \times (-2) = 4 = (2)^2$$

$$\sqrt{4} = -2; \ \ \ \ \ \sqrt{4} = 2$$

$$\sqrt{4} = \pm 2$$

(ii) $$(-5)^2 = (-5) \times (-5) = 25 = (5)^2$$

$$\sqrt{25} = -5; \ \ \ \ \ \sqrt{25} = 5$$

$$\sqrt{25} = \pm 5$$

Therefore, the square root of a number can be written as $\sqrt{x}=±\phantom{\rule{0.147em}{0ex}}y$. That is,

$\begin{array}{l}\sqrt{4}=±\phantom{\rule{0.147em}{0ex}}2\\ \\ \sqrt{25}=\phantom{\rule{0.147em}{0ex}}±\phantom{\rule{0.147em}{0ex}}5\end{array}$

But in this chapter, we will only learn about the positive roots.

Now the following table consists of squares and square roots of the first $$20$$ numbers.

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