## Radical Equations:

__Objective__: Solve radical equations.__Radical Equation__: a radical equation contains a variable within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a power.A "radical" equation is an equation in which at least one variable expression is stuck inside a radical, usually a square root.

The "radical" in "radical equations" can be any root, whether a square root, a cube root, or some other root. Most of the examples in what follows use square roots as the radical, but (warning!) you should not be surprised to see an occasional cubed root or higher in your homework or on a test.

In general, you "solve" equations by "isolating" the variable; you isolate the variable by "undoing" whatever had been done to it, just like you do when you solve a regular equation.

The "radical" in "radical equations" can be any root, whether a square root, a cube root, or some other root. Most of the examples in what follows use square roots as the radical, but (warning!) you should not be surprised to see an occasional cubed root or higher in your homework or on a test.

In general, you "solve" equations by "isolating" the variable; you isolate the variable by "undoing" whatever had been done to it, just like you do when you solve a regular equation.

## Steps to Solving a Radical Equation

1. Isolate the variable.

2. Raise both sides of the equation to the power equal to the index of the radical.

3. Simplify and solve.

4. Check

2. Raise both sides of the equation to the power equal to the index of the radical.

3. Simplify and solve.

4. Check

__answers.__**ALL**