Question

how would you solve the equation (x+3)^{3/2}-11=53? what is the correct solution?

Answer 1

\[\begin{align*}
(x+3)^{3/2}-11&=53\\
(x+3)^{3/2}&=64\\
\left((x+3)^{3/2}\right)^{2/3}&=(64)^{2/3}\\
x+3&=(64)^{2/3}\\
&~\vdots
\end{align*}\]

Answer 2

\[(x+3)^{3/2}-11=53 \rightarrow (x+3)^{3/2}=53+11 \rightarrow (x+3)^{3/2}=64\]
i.e. \[(x+3)=64^{2/3} \rightarrow (x+3)=(4^3)^{2/3} \]
i.e. \[ (x+3)=(4^2) \rightarrow x+3=16 \rightarrow x= 16-3 \rightarrow x=13\]