Solve. $LaTeX: \displaystyle \sqrt{x + 16}=\sqrt{x - 8} + 4$

Squaring both sides gives $LaTeX: \displaystyle x + 16=x + 8 \sqrt{x - 8} + 8$ . Isolating the radical gives $LaTeX: \displaystyle 1=\sqrt{x - 8}$ Squaring again gives $LaTeX: \displaystyle 1=x - 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=9$ . Checking the solution, $LaTeX: \displaystyle x = 9$ , in the original equation gives $LaTeX: \displaystyle 5 = 5$ which is true so the solution checks.