√50
Show answer
5√2
Free printable worksheet
Radical Expressions Worksheet
Twenty problems simplifying, combining, multiplying, and rationalizing radicals.
Algebra 1Grades 8-113 pagesAnswer key included
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What this worksheet includes
- Twenty problems simplifying, combining, multiplying, and rationalizing radicals.
- 3-page printable PDF with a complete answer key
- Designed for Grades 8-11 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this radical expressions worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 8-11 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach radical expressions
A radical is simplified by separating its radicand into a perfect-square factor and a remaining factor. Only like radicals—those with the same index and radicand—can be combined.
Multiplication may create a new perfect-square factor, while rationalizing removes a radical from a denominator. Check that no perfect-square factor remains under the radical sign.
Learning objectives
- Simplify square roots
- Combine like radicals
- Multiply radicals and rationalize denominators
Skills to review first
- Perfect squares
- Prime factorization
- Combining like terms
Worked example
Follow the reasoning step by step
Simplify √72.
- Factor 72 as 36 · 2.
- Use √72 = √36 · √2.
- Evaluate √36 = 6.
- Write 6√2.
Solution: 6√2.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
3√8 + √18
Show answer
9√2
√5 · √20
Show answer
10
Error check
Common mistakes to watch for
- Splitting a square root across addition
- Combining radicals with different radicands
- Stopping before simplifying the radicand completely