Exponents and radicals
Adding and subtracting radicals worksheets
Choose already simplified radicals, simplify-one, simplify-all or mixed problems for 10 sums and differences. Select unit, nonunit or mixed coefficients.
Preview and downloadExponents and radicals practice
Radical expression operations worksheets
Generate 10 mixed addition, subtraction and multiplication problems with independently selectable Easy, Medium and Hard profiles. Numeric practice progresses from two to three visible radical terms; Hard problems use x with x > 0 and include genuine trinomial products.
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Start with a ready-made worksheet
Simplify first, then add, subtract, or distribute and multiply. Assume x > 0 when x appears.
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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.
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Learning objective
What this activity builds
Simplify radical monomials, combine like radicals and distribute products while preserving exact values on the stated positive-variable domain.
Worked example
Simplify 2√12 + √27.
7√3.
Extract the square factors: 2√12 = 4√3 and √27 = 3√3. The radical parts now match, so their coefficients add to 7.
Teaching notes
Make the practice count
- Name the operation before simplifying.
- Extract square factors from every radical before combining terms.
- Combine only terms with matching simplified radical parts.
- For a product, distribute the monomial to every term in the second factor.
- Use x > 0 when simplifying products of radicals containing x.
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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.
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Print 10 monomial-by-monomial, monomial-by-binomial or binomial-by-binomial radical products. Choose coefficient types and practice distributing before simplifying.
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Exponents and radicals
Simplifying radical expressions worksheets
Practice 10 numeric-only, variable-only or mixed radicals with square, cube, fourth, fifth or sixth roots. Extract perfect powers and use absolute values where even roots require them.
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