a) \(\left(x-\dfrac{1}{2}\right)^2=0\Leftrightarrow x-\dfrac{1}{2}=0\Leftrightarrow x=\dfrac{1}{2}\) vậy \(x=\dfrac{1}{2}\)

b) \(\left(x-2\right)^2=1\Leftrightarrow\left[{}\begin{matrix}x-2=\sqrt{1}\\x-2=-\sqrt{1}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

vậy \(x=3;x=1\)

c) \(\left(2x-1\right)^3=-8\Leftrightarrow2x-1=\sqrt[3]{-8}=-2\Leftrightarrow2x=-1\)

\(\Leftrightarrow x=\dfrac{-1}{2}\) \(\) vậy \(x=\dfrac{-1}{2}\)

d) \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\sqrt{\dfrac{1}{16}}\\x+\dfrac{1}{2}=-\sqrt{\dfrac{1}{16}}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{4}\\x=\dfrac{-3}{4}\end{matrix}\right.\) vậy \(x=\dfrac{-1}{4};x=\dfrac{-3}{4}\)