Radical Equations

Front

What is a radical equation?

Back

An equation that contains a variable within a radical (square root, cube root, etc.).

Front

How do you isolate a radical in an equation?

Back

To isolate a radical, move all other terms to the opposite side of the equation.

Front

What is the first step in solving a radical equation?

Back

Square both sides of the equation to eliminate the radical.

Front

What should you do after squaring both sides of a radical equation?

Back

Solve the resulting equation for the variable.

Front

What is a common mistake when solving radical equations?

Back

Forgetting to check for extraneous solutions after solving.

Front

What is an extraneous solution?

Back

A solution that does not satisfy the original equation.

Front

How can you check if a solution is extraneous?

Back

Substitute the solution back into the original equation.

Front

What is the domain of a radical function?

Back

The set of all possible input values (x) for which the function is defined.

Front

What is the importance of checking solutions in radical equations?

Back

To ensure that the solutions are valid and not extraneous.

Front

What does it mean to simplify a radical?

Back

To express the radical in its simplest form, removing any perfect squares from under the radical.