Radical Expressions
A free Algebra II lesson from the “Rational Exponents and Radicals” unit, with a worked example and practice problems including step-by-step solutions.
Radical expressions involve roots, most often square roots. Simplifying radicals means pulling out perfect-square factors while leaving the non-square part inside the radical. This matters because simplified radical form makes expressions easier to compare, combine, and solve. When practicing, factor the radicand into a perfect square times a leftover factor, then take the square root of the perfect square. A common mistake is splitting addition inside a radical, such as treating sqrt(a + b) like sqrt(a) + sqrt(b). That property does not work.
What you'll learn
- Simplify square roots
- Use perfect-square factors
- Combine like radicals
Worked example
Problem. Simplify sqrt(72).
- 72 = 36 x 2.
- sqrt(36) = 6.
- sqrt(72) = 6sqrt(2).
Answer: 6sqrt(2)
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Simplify sqrt(50).
Show solution
- 50 = 25 x 2.
Answer: 5sqrt(2)
2. Simplify sqrt(48).
Show solution
- 48 = 16 x 3.
Answer: 4sqrt(3)
3. Simplify 2sqrt(5) + 3sqrt(5).
Show solution
- Add coefficients of like radicals.
Answer: 5sqrt(5)
4. Simplify sqrt(18) + sqrt(8).
Show solution
- sqrt(18)=3sqrt(2) and sqrt(8)=2sqrt(2).
Answer: 5sqrt(2)
5. Which radical is already simplified?
Choices: sqrt(7) · sqrt(12) · sqrt(20) · sqrt(45)
Show solution
- 7 has no perfect-square factor other than 1.
Answer: sqrt(7)
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