For the question in the image, can someone please explain to me why we should interpret $\sqrt{x^2}$ as $|x|$?
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$x\geq 0 \Rightarrow \sqrt{x^2} = x\\x< 0 \Rightarrow \sqrt{x^2} = -x\\ \text{This is identical to the definition of }|x|$
graph of $y = \sqrt{x^2}$
The definition of the symbol $\sqrt{x}$ is that it is the positive square root.
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