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 radical in an equation?

Back

To isolate a radical, you can move all other terms to the opposite side of the equation, leaving the radical alone on one side.

Front

Back

Multiply both sides by 4 to eliminate the fraction.

Front

Back

x = 4.

Front

What is the principle of squaring both sides of an equation?

Back

Squaring both sides of an equation can eliminate the radical, but it may introduce extraneous solutions.

Front

Back

x = 13/2.

Front

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

Back

Check for extraneous solutions by substituting back into the original equation.

Front

Back

x = 4 or x = 0 (check for extraneous solutions).

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that does not satisfy the original equation after checking.

Front

Back

Graph the functions y = ext{sqrt}(3x + 2) and y = 4, and find their intersection points.