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 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 verify.

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

What is the importance of checking solutions in radical equations?

Back

To ensure that the solutions are valid and not extraneous.

Front

Solve the equation: √(x + 3) = 5.

Back

x = 22.