1) Solve for \(x\). \(\sqrt{x-1}+\sqrt{2x}=3\)
2) Solve for \(x\). \(\sqrt{x+16}=\ \sqrt{x}+4\)
3) Find the slope of the line. \(9y-4x=y\sqrt{21}+x\sqrt{7}+3\)
4) Solve for \(x\). \(\sqrt{x-1}+\sqrt{x}=\ \large\frac{8}{\sqrt{x-1}}\)
5) Solve the system of equations.
\({\begin{cases} y=\sqrt[4]{5x+36} \\ y=\sqrt x \\\end{cases}}\)
6) Solve the system of equations.
\({\begin{cases} y=\sqrt[4]x\\ y=\sqrt[8]{15x+16}\\\end{cases}}\)
7) Given \(f\left(x\right)=\sqrt{x+2}\) solve for \(k\) if \(f\left(k+2\right)=1+f\left(k-1\right)\).
8) Find all ordered triples \( (a,b,c) \) such that:
\(
\begin{cases}
\sqrt{ab} + \sqrt{bc} = 9 \\
\sqrt{ac} + \sqrt{ab} = 5 \\
\sqrt{bc} + \sqrt{ac} = 8 \\
\end{cases}
\)
9) Find a simplified expression for \( \sqrt{12 + \sqrt{12 + \sqrt{12 + ...}}} \)
10) Solve: \( \sqrt[4]{\frac{2-x}{3+x}} + \sqrt[4]{\frac{3+x}{2-x}} =2 \)
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