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Exponents and radicals practice

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.

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Simplify every radical that needs it. Combine like radical terms and leave unlike radical parts separate.

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US Letter

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A4

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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 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

Simplify radicals first and combine coefficients only when the remaining radical parts match.

Worked example

Simplify √50 − √8.

3√2.

√50 = 5√2 and √8 = 2√2. The radical parts match, so subtract their coefficients: (5 − 2)√2.

Teaching notes

Make the practice count

  • Underline matching radical parts after simplifying.
  • Start with already simplified terms to isolate the combining rule.
  • Include unlike terms so learners do not force every sum into one radical.
  • Check the sign of each coefficient before combining.

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Math SheetNameScore/ 10TeacherDateAdd and Subtract RadicalsSimplify and combine like radical terms.1.2-5·22.2·45-1·5+2·53.96-2·1504.2·3-1·3+3·25.40-6·106.2·18-1·32+3·507.6-5·68.4·125-1·5+4·69.12-2·2710.6·7-1·7+3·7math-sheet.comPage 1 / 1

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