√81
Show answer
9
Free printable worksheet
Square Roots Worksheet
Twenty square-root problems using perfect squares, estimation, and inverse operations.
Middle School MathGrades 7-83 pagesAnswer key included
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What this worksheet includes
- Twenty square-root problems using perfect squares, estimation, and inverse operations.
- 3-page printable PDF with a complete answer key
- Designed for Grades 7-8 middle school math practice
- Available as an immediate free download with no email required
How to use it
Use this square roots 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 7-8 students working on middle school math. 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 Middle School Math worksheets.
Topic guide
How to approach square roots
The principal square root of a number is the nonnegative value that squares to produce it. Perfect squares have whole-number roots; other roots can be estimated between nearby perfect squares.
A square-root symbol by itself names one nonnegative value, while solving x² = a usually produces both positive and negative solutions.
Learning objectives
- Evaluate perfect square roots
- Estimate non-perfect square roots
- Connect squares and square roots
Skills to review first
- Multiplication facts
- Exponent notation
- Ordering decimals
Worked example
Follow the reasoning step by step
Evaluate √144.
- Ask which nonnegative number squared equals 144.
- Recall 12 × 12 = 144.
- Use the principal, nonnegative root.
- Check 12².
Solution: 12.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
Between which integers is √50?
Show answer
7 and 8
Solve x² = 49.
Show answer
x = 7 or x = −7
Error check
Common mistakes to watch for
- Dividing the radicand by 2
- Writing ± for the principal square-root expression
- Using nonconsecutive perfect squares for an estimate