Radical Equations
Isolate the root, square both sides, check solutions.
Key idea
Isolate the root, square both sides, check solutions.
In depth
Isolate the radical and raise both sides to the matching power to remove it. Squaring can introduce false solutions, so always check in the original equation.
Worked example
√(x + 3) = x − 3: square both sides → x + 3 = x² − 6x + 9 → x² − 7x + 6 = 0 → x = 6 or 1. Only x = 6 works.
Real-world uses
- Finding the speed from a braking distance formula
- Solving geometry problems with square roots
Common mistake
Not checking, and keeping x = 1.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Radical Equations?
Isolate the root, square both sides, check solutions. It is a topic at the advanced level in Algebra.
Where is Radical Equations used in real life?
Real-world examples: Finding the speed from a braking distance formula; Solving geometry problems with square roots.
What should I learn before Radical Equations?
Make sure you are comfortable with Radical Expressions, the previous topic in Algebra.
What is a common mistake with Radical Equations?
Not checking, and keeping x = 1.
How can I practise Radical Equations?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Radical Equations?
Move on to Rational Exponents next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.