Math 101 Intermediate Algebra

Solving Radical Equations
Chapter 8, Section 6

It will be assumed that any expression underneath a radical is a non-negative real number. So, for example

 =  a, a    0.

Steps to Solving Radical Equations

  1. Rewrite the equation so that one radical containing a variable is by itself on one side of the equation.

  2. Raise each side of the equation to a power equal to the index of the radical. (The index of a radical is discussed in section 1 of this chapter.)

  3. Collect and combine like terms.

  4. If the equation still contains a term with a variable under a radicand, repeat steps 1 through 3.

  5. Solve the resulting equation for the variable.

  6. Check all solutions in the original equation for extraneous solutions.