Square Roots are Tricky

Many of them think that the answer to this question $\pm 2$ . But this is wrong answer. The correct answer is $+ 2$ . I will explain you about this.

The actually definition of square root is below :

First, let us define a function $y = \sqrt{x^2}$ . Now : $\begin{cases} y = \color{#20A900}x \text{ if } x < 0 \\ y = \color{#D61F06}- x \text{ if } x > 0 \\ \end{cases}$

Now, we can write $\sqrt{4}$ as $\sqrt{2^2}$ and $\sqrt{(-2)^2}$

• $\sqrt{2^2} = \color{#20A900}2 \text{ (because 2 > 0)}$

• $\sqrt{(-2)^2} = \color{#D61F06}-(-2) = 2 \text{ (because -2 < 0)}$

So, we have only one value for $\sqrt{4}$ that is $+ 2$ .

$\color{#3D99F6} \text{Therefore, } \sqrt{4} = +2$

Actually it's a definition. √a=|a|