Strategy for Solving Equations with Radicals

 

Step 1.  Simplify both expressions as much as possible.

 

Step 2.  Isolate one radical on one side of the equation; that is, use the Addition Property of Equality and the Multiplication Property of Equality to get one radical on one side of the equation by itself.

 

Step 3.  Raise both sides of the equation to a power equal to the index of the radical.

 

Step 4.  Simplify both expressions as much as possible.

 

Step 5.  Repeat Steps 2, 3, and 4 until there are no more radicals.

 

At this point, the problem has been reduced to solving either a polynomial equation or an equation with rational expressions.