Radical equation

Definition

A radical equation is an equation in which the variable is contained within a radical, such as a square root or cube root. Solving these equations typically involves isolating the radical and then eliminating it by raising both sides of the equation to a power.

5 Must Know Facts For Your Next Test

1. To solve a radical equation, isolate the radical on one side of the equation.
2. After isolating the radical, eliminate it by raising both sides of the equation to the appropriate power (e.g., squaring if it's a square root).
3. Check for extraneous solutions because raising both sides to a power can introduce solutions that do not satisfy the original equation.
4. If an equation contains more than one radical term, you may need to isolate and eliminate them one at a time.
5. $\sqrt{x + 3} = x - 1$ is an example of a simple radical equation.

Review Questions

• What are the steps to solve a radical equation?
• Why is it important to check for extraneous solutions in radical equations?
• Solve: $\sqrt{2x + 5} = x - 1$.

Related terms

Radical: An expression that includes a root symbol, such as $\sqrt{}$ or $\sqrt[3]{}$, indicating the extraction of roots.

Extraneous Solution: A solution derived from an algebraic manipulation that does not satisfy the original equation.

Isolate: The process of getting a variable or term alone on one side of an equation.