# Why are solutions to square roots positive and negative?

Given a positive real number a, there are two solutions to the equation ${x}^{2} = a$, one is positive, and the other is negative. We denote the positive root (which we often call the square root) by $\setminus \sqrt{a}$. The negative solution of ${x}^{2} = a$ is −\sqrt{a} (we know that if $x$ satisfies ${x}^{2} = a$, then (−x)^2=x^2=a, therefore, because $\setminus \sqrt{a}$ is a solution, so is −\sqrt{a}). So, for $a > 0 , \setminus \sqrt{a} > 0$, but there are two solutions to the equation ${x}^{2} = a$, one positive $\left(\setminus \sqrt{a}\right)$ and one negative (−\sqrt{a}). For $a = 0$, the two solutions coincide with $\setminus \sqrt{a} = 0$.
PS . note that something like $\sqrt{- 1}$ wouldn't exist as we know that 2 integers with opposite symbols will not give a negative number.And for it to be a square number both the nos . have to be same.