Answer Key 9.11
First, the roots:
![\[\begin{tabular}{|c|c|c|} \hline \begin{array}{ccc}&3& \\ &\textbf{44}& \\ 8&&4\end{array}& \begin{array}{ccc}&9& \\ &\textbf{32}& \\ 7&&2\end{array}& \begin{array}{ccc}&8& \\ &\textbf{75}& \\ 7&&\sqrt{x} \end{array}\\ \hline \end{tabular}\]](https://pressbooks.bccampus.ca/intermediatealgebrakpu/wp-content/ql-cache/quicklatex.com-a19690c1971154d9535aad1a7ec849b2_l3.png "Rendered by QuickLaTeX.com")
Check for pattern in the first box:
Check #3 pattern with the next box:
![\[(7+9)\cdot 2=32\checkmark\]](https://pressbooks.bccampus.ca/intermediatealgebrakpu/wp-content/ql-cache/quicklatex.com-3e8c1645ddb8b848d604bc9cb256bda3_l3.png "Rendered by QuickLaTeX.com")
Finally:
![\[\begin{array}{rrl} (7+8)\sqrt{x}&=&75 \\ \\ 15\sqrt{x}&=&75 \\ \\ \dfrac{15}{15}\sqrt{x}&=&\dfrac{75}{15} \\ \\ \sqrt{x}&=&5 \\ \\ \therefore (\sqrt{x})^2&=&(5)^2 \\ \\ x&=&25 \end{array}\]](https://pressbooks.bccampus.ca/intermediatealgebrakpu/wp-content/ql-cache/quicklatex.com-c16c90724284999e9b6a5d96062a3fa1_l3.png "Rendered by QuickLaTeX.com")
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