Solving Radical Equations

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Front

How do you isolate a variable in a radical equation?

Back

To isolate a variable, you can perform inverse operations, such as squaring both sides to eliminate a square root.

Front

Back

Raise both sides to the power of 3.

Front

What does it mean to 'undo' a square root in an equation?

Back

To 'undo' a square root means to square both sides of the equation.

Front

Back

x = 17.

Front

Back

x = 8.

Front

Back

Add 1 to both sides.

Front

Back

x = 61.

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions is important because squaring both sides can introduce extraneous solutions that do not satisfy the original equation.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.