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

What is the first step in solving a radical equation?

Back

The first step is often to isolate the radical on one side of the equation.

Front

How do you eliminate a square root in an equation?

Back

You can eliminate a square root by squaring both sides of the equation.

Front

Back

The solution is when the numerator equals zero, provided the denominator is not zero.

Front

Back

Set the numerator equal to zero and solve for the variable.

Front

Back

Set the numerator equal to the denominator and solve for the variable.

Front

Back

Cross-multiply to solve for the variable.

Front

Back

Cross-multiply and simplify to find the variable.

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions is important because squaring both sides can introduce extraneous solutions.

Front

What is an extraneous solution?

Back

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