Exponents and radicals
Square and cube equations worksheets
Generate 18 equations with squared, cubed or rooted variables. Set magnitudes from 1 to 20, choose equation types and select the signs of cubic values.
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Perfect squares and cubes worksheets
Create 18 questions on squares, cubes, square roots or cube roots. Set a base or root magnitude range from 1 to 20 and choose powers, roots or both.
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Evaluate each power or root. The chosen range applies to the base of a power or the answer magnitude of a root.
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Choose one challenge at a time
Start with a focused choice of operations or expression types. Combine them when the learner can explain the rule being used, as well as calculate the result.
Read the domain printed on variable problems. A simplified expression must keep any values excluded by the original denominator or radical.
The selected range applies to the base or root magnitude, not the powered result. A very narrow range may intentionally repeat facts to keep the full 18-question practice set.
The preview and downloaded PDF use the same resolved questions. Answers follow on separate pages; choose the student-only edition when handing out the exercise.
Learning objective
What this activity builds
Recall and connect perfect squares and cubes with their inverse root operations.
Worked example
How are 7³ and the cube root of 343 connected?
7³ = 343 and ∛343 = 7.
Cubing multiplies three equal factors. Taking the real cube root reverses that operation.
Teaching notes
Make the practice count
- Start with a narrow range to build recall.
- Pair each power with its inverse root.
- Mix squares and cubes only after the notation is familiar.
- A one-value range intentionally repeats the available facts.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose the mathematical settings. Every worksheet is balanced, reproducible, and checked with exact arithmetic.
Enlarged pages scroll. PDF size stays the same.
A useful next step
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Simple integer exponents worksheets
Generate 20 powers using positive or negative integer bases. Choose any exponent values from −4 through 5, including zero and negative powers, with a separate answer key.
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