Are the following expressions are equal?
$$\sqrt{x^2}=(\sqrt{x})^2=|x|$$
As there both are: $$x^\frac{2}{2}=x^1$$
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No.
$\sqrt{x^2}=(\sqrt{x})^2$ is not true.
Consider the domain of $\sqrt{x^2}$ are all real numbers, but $(\sqrt{x})^2$ is $x\geq 0$. So $\sqrt{x^2}\neq(\sqrt{x})^2$.
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So for $0 /leq x$ it is true? – gbox Jun 03 '15 at 10:43
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@gbox Yes, it is true when $x\geq 0$. – Eff Jun 03 '15 at 10:45
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@gbox for $x\geq 0$ it is – Jun 03 '15 at 10:45