Simplifying Radicals Worksheet (Simplify Square Roots)
Simplifying radicals is one of the most important square root topics in middle school and early Algebra. Students often understand perfect squares like $$\sqrt{49}=7$$, but they get stuck when the number under the radical is not a perfect square. That is where simplifying comes in.
This free printable simplifying radicals worksheet helps students practice rewriting square roots in simplest form by finding the largest perfect square factor. The goal is simple: pull perfect squares out of the radical, and leave the remaining factor inside.
What does it mean to simplify a radical?
A radical is simplified when there are no perfect square factors left under the square root. In simplest radical form, answers are usually written as a whole number coefficient outside the radical times a simplified square root inside the radical.
For example, $$\sqrt{72}$$ is not in simplest form because 72 contains a perfect square factor (36). Once you rewrite it as $$\sqrt{36\cdot 2}$$, you can simplify:
$$\sqrt{72}=\sqrt{36\cdot 2}=6\sqrt{2}$$
That same idea applies to every problem on this worksheet.
What students practice on this worksheet
This worksheet includes 16 problems that build fluency with common square roots that simplify neatly. Students practice:
- spotting perfect square factors (4, 9, 16, 25, 36, 49, 64, 100)
- rewriting radicals as a product
- simplifying to a coefficient times a radical
- keeping answers in simplest radical form
Because the problems are presented in a clean two-column layout, this worksheet works well for classwork, homework, warm-ups, or quiz review.
How to use this worksheet
Here are a few simple ways teachers and families use this resource:
- Guided practice: do the first 2–3 problems together, then students finish independently
- Homework: assign all 16 for steady practice
- Quick check: assign only the even-numbered problems
- Small group support: focus on numbers that share the same perfect square factor (like 50, 75, 200)
An answer key is included so students can check work and teachers can grade quickly. The answer key also shows the factoring step, which helps students understand why the simplification works.
Extend the skill
Once students can simplify numerical radicals, the next natural step is to simplify radicals with variables and then move into multiplying and dividing radical expressions. If your student is comfortable with the problems on this page, they are ready for:
- simplifying radicals with variables
- multiplying radicals (then simplifying)
- dividing radicals and rationalizing the denominator
