Solving 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 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 to see if it holds true.

Front

What is the solution to the equation √(x + 4) = 6?

Back

x = 32.

Front

What is the solution to the equation √(2x - 8) = 4?

Back

x = 12.

Front

What happens if you square both sides of an equation incorrectly?

Back

You may introduce extraneous solutions or change the equation's meaning.