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:

1. [latex]3\cdot 8+4=28[/latex]
2. [latex]4\cdot 8\cdot 3=35[/latex]
3. [latex](8+3)\cdot 4=44\checkmark[/latex]

Check #3 pattern with the next box:

\[(7+9)\cdot 2=32\checkmark\]

Finally:

\[\begin{array}{rrl}
(7+8)\sqrt{x}&=&75 \\ \\
15\sqrt{x}&=&75 \\ \\
\dfrac{15}{15}\sqrt{x}&=&\dfrac{75}{15} \\ \\
\sqrt{x}&=&5 \\ \\
\therefore (\sqrt{x})^2&=&(5)^2 \\ \\
x&=&25
\end{array}\]