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

Squaring both sides gives $LaTeX: \displaystyle x + 16=x + 8 \sqrt{x + 8} + 24$ . Isolating the radical gives $LaTeX: \displaystyle -1=\sqrt{x + 8}$ Squaring again gives $LaTeX: \displaystyle 1=x + 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=-7$ . Checking the solution, $LaTeX: \displaystyle x = -7$ , in the original equation gives $LaTeX: \displaystyle 3 = 5$ which is false so it is an extraneous solution and there is no solution.