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, you can 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

Simplify the equation and solve for the variable.

Front

What is a common mistake when solving radical equations?

Back

Forgetting to check for extraneous solutions after solving.

Front

What does it mean if a radical equation has no solution?

Back

It means that there are no values for the variable that satisfy the equation.

Front

How can you check if your solution to a radical equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving the equation but does not satisfy the original equation.

Front

Solve the radical equation: √(x + 9) = 5.

Back

x = 16.

Front

Solve the radical equation: √(2x - 4) = 6.

Back

x = 28.