Answer Key 9.11
First, the roots:
\begin{tabular}{|c|c|c|}
\hline
\begin{array}{ccc}&3& \\ &\textbf{44}& \\ 8&&4\end{array}&
\begin{array}{ccc}&9& \\ &\textbf{32}& \\ 7&&2\end{array}&
\begin{array}{ccc}&8& \\ &\textbf{75}& \\ 7&&\sqrt{x} \end{array}\\
\hline
\end{tabular}
Check for pattern in the first box:
- 3⋅8+4=28
- 4⋅8⋅3=35
- (8+3)⋅4=44✓
Check #3 pattern with the next box:
(7+9)⋅2=32✓
Finally:
\begin{array}{rrl} (7+8)\sqrt{x}&=&75 \\ \\ 15\sqrt{x}&=&75 \\ \\ \dfrac{15}{15}\sqrt{x}&=&\dfrac{75}{15} \\ \\ \sqrt{x}&=&5 \\ \\ \therefore (\sqrt{x})^2&=&(5)^2 \\ \\ x&=&25 \end{array}