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 solve a radical equation?

Back

Isolate the radical on one side, then square both sides to eliminate the radical, and solve for the variable.

Front

What is the importance of checking your solution in radical equations?

Back

To ensure that the solution does not produce extraneous solutions, which are false solutions introduced when squaring both sides.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving an equation but is not a valid solution to the original equation.

Front

Example of a simple radical equation: √(x + 3) = 5. What is x?

Back

x = 22.

Front

What happens when you square both sides of an equation?

Back

You eliminate the radical, but you must check for extraneous solutions afterward.

Front

If √x = 4, what is x?

Back

x = 16.

Front

What is the domain of a radical function?

Back

The set of all possible input values (x) for which the function is defined, typically x must be greater than or equal to zero for square roots.

Front

How do you graph a radical function?

Back

Start by plotting key points, such as the vertex, and then sketch the curve, which typically increases slowly.

Front

What is the square root property?

Back

If x² = a, then x = ±√a.