Question Number 14811 by Nayon last updated on 04/Jun/17
$${why}\:\:\:\:\:\sqrt{{x}^{\mathrm{2}} }=\mid{x}\mid\:\:\:\:?\: \\ $$
Answered by mrW1 last updated on 04/Jun/17
$${if}\:{x}\geqslant\mathrm{0},\:\sqrt{{x}^{\mathrm{2}} }={x}=\mid{x}\mid \\ $$$${if}\:{x}<\mathrm{0},\:\sqrt{{x}^{\mathrm{2}} }=\sqrt{\left(−{x}\right)^{\mathrm{2}} }=\left(−{x}\right)=\mid{x}\mid \\ $$$$\Rightarrow\sqrt{{x}^{\mathrm{2}} }=\mid{x}\mid\:\left({always}\:{valid}\right) \\ $$