Rational and Radical Checkpoint
A free College Algebra lesson from the “Rational Expressions and Equations” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint reviews exponent rules, radicals, rational expressions, rational equations, coordinate formulas, and conic basics.
What you'll learn
- Simplify radicals and rational expressions
- Solve rational and radical equations
- Use exponent rules
Worked example
Problem. Simplify (x^2 - 16)/(x - 4).
- Factor x^2 - 16.
- Cancel x - 4.
- Keep x != 4 as a restriction.
Answer: x + 4, x != 4
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Simplify sqrt(75).
Show solution
- 75 = 25 x 3.
Answer: 5sqrt(3)
2. Simplify (x^2 - 36)/(x - 6).
Choices: x + 6, x != 6 · x - 6 · x + 6, x != -6 · x^2 + 6
Show solution
- Factor difference of squares.
Answer: x + 6, x != 6
3. Solve 15/(x + 2) = 5.
Show solution
- 15 = 5(x + 2).
Answer: 1
4. Find the distance between (0, 0) and (5, 12).
Show solution
- Use the 5-12-13 triangle.
Answer: 13
5. Simplify x^4 * x^3.
Choices: x^7 · x^12 · x · 2x^7
Show solution
- Add exponents with the same base.
Answer: x^7
Practice this interactively with instant feedback and an AI tutor.
Practice Rational and Radical Checkpoint Take the free placement check