1) \(\left(x-1\right)^3=\dfrac{1}{8}\)
\(\Rightarrow\left(x-1\right)^3=\left(\dfrac{1}{2}\right)^3\)
\(\Rightarrow x-1=\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{1}{2}+1\)
\(\Rightarrow x=\dfrac{3}{2}\)
2) \(\left(3-x\right)^3=-\dfrac{27}{64}\)
\(\Rightarrow\left(3-x\right)^3=\left(-\dfrac{3}{4}\right)^3\)
\(\Rightarrow3-x=-\dfrac{3}{4}\)
\(\Rightarrow x=3+\dfrac{3}{4}\)
\(\Rightarrow x=\dfrac{15}{4}\)
3) \(\left(x-5\right)^3=-\dfrac{1}{27}\)
\(\Rightarrow\left(x-5\right)^3=\left(-\dfrac{1}{3}\right)^3\)
\(\Rightarrow x-5=-\dfrac{1}{3}\)
\(\Rightarrow x=-\dfrac{1}{3}+5\)
\(\Rightarrow x=\dfrac{14}{3}\)
4) \(\left(x-4\right)^2=\dfrac{4}{9}\)
\(\Rightarrow\left(x-4\right)^2=\left(\dfrac{2}{3}\right)^2\)
\(\Rightarrow x-4=\dfrac{2}{3}\)
\(\Rightarrow x=\dfrac{2}{3}+4\)
\(\Rightarrow x=\dfrac{14}{3}\)
5) \(\left(5-x\right)^2=\dfrac{1}{16}\)
\(\Rightarrow\left(5-x\right)^2=\left(\dfrac{1}{4}\right)^2\)
\(\Rightarrow5-x=\dfrac{1}{4}\)
\(\Rightarrow x=5-\dfrac{1}{4}\)
\(\Rightarrow x=\dfrac{19}{4}\)
6) \(\left(x+1\right)^2=\dfrac{4}{49}\)
\(\Rightarrow\left(x+1\right)^2=\left(\dfrac{2}{7}\right)^2\)
\(\Rightarrow x+1=\dfrac{2}{7}\)
\(\Rightarrow x=\dfrac{2}{7}-1\)
\(\Rightarrow x=-\dfrac{5}{7}\)
