Radical equation

Definition

A radical equation is an equation in which the unknown variable appears under a radical sign, most commonly a square root. Solving these equations typically involves isolating the radical expression and then squaring both sides to eliminate the radical.

5 Must Know Facts For Your Next Test

1. To solve a radical equation, isolate the radical on one side of the equation before squaring both sides.
2. Always check for extraneous solutions by substituting back into the original equation because squaring both sides can introduce invalid solutions.
3. Radical equations can sometimes require more than one iteration of isolating and squaring radicals if there are multiple radicals present.
4. In some cases, you may need to apply higher-order roots or exponents if dealing with cube roots or other radicals.
5. Simplifying expressions under the radical before solving can make the process easier and reduce errors.

Review Questions

• What is the first step in solving a radical equation?
• Why is it important to check for extraneous solutions when solving radical equations?
• How would you handle an equation with more than one radical term?

Related terms

Extraneous Solution:

A solution derived from an algebraic manipulation that is not a true solution of the original equation.

Isolate: The process of manipulating an equation to get a specific variable or term alone on one side of the equation.

Square Root:

$\text{If } x^2 = y, \text{ then } x \text{ is called a square root of } y.$