Radical Equations

Solve the following two equations by isolating the radical on one side and squaring both sides:
$\sqrt{2x+1}5=2$
$\sqrt{2x+1}+5=2$
Be sure to check your solutions.

If we raise both sides of an equation a power, we sometimes obtain an equation which has more solutions than the original one. (Sometimes the extra solutions are called extraneous solutions.) Which of the following equations result in extraneous solutions when you raise both sides to the indicated power ? Explain.
$\sqrt{x}=5$, square both sides
$\sqrt{x}=5$, square both sides
$\sqrt[3]{x}=5$, cube both sides
$\sqrt[3]{x}=5$, cube both sides

Create a square root equation similar to the one in part (a) that has an extraneous solution. Show the algebraic steps you would follow to look for a solution, and indicate where the extraneous solution arises.