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

Why is it important to check your solutions in radical equations?

Back

To ensure that the solutions do not produce extraneous results, which are false solutions introduced during the squaring process.

Front

What is an extraneous solution?

Back

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

Front

Solve: √(x + 5) = 7. What is x?

Back

x = 44.

Front

Solve: √(2x - 3) = 5. What is x?

Back

x = 4.

Front

Solve: √(x - 1) + 3 = 6. What is x?

Back

x = 10.

Front

Solve: √(x + 4) = -2. What is the solution?

Back

No solution, since a square root cannot be negative.

Front

What is the first step in solving √(x) = 9?

Back

Square both sides to eliminate the radical: x = 81.

Front

If √(x) = 0, what is x?

Back

x = 0.