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