Two Different solutions for the same equation

Question

$\sqrt{x}\sqrt{x}=4$ then $x=4$

But $\sqrt{x}\sqrt{x}=\sqrt{x^2}$

So, $\sqrt{x^2}=4$ which leads to $|x|=4$.

Why is this happening?

Answer 1

The equality $\sqrt x\times \sqrt x=\sqrt {x^2}$ is valid only if $x\ge 0$; therefore$$\sqrt{x^2}=|x|=x=4$$

Answer 2

Before starting solving an equation with square roots, you have to put the C.E (condition of existance) of the radicants. In this case $x\geq0$, so the solution $x=-4$ isn't acceptable.