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Exponents and radicals practice

Simplifying square roots worksheets

Generate 10 square-root problems using perfect squares, nonperfect radicands or outside coefficients. Practice exact factor extraction with a separate answer key.

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Worksheet · LetterWorksheet · A4
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Simplify each square root exactly. Extract perfect-square factors and multiply them by any coefficient already outside the radical.

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US Letter

Student worksheetWorksheet with answers

A4

Student worksheetWorksheet with answers
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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

Find the largest perfect-square factor of a radicand and express its square root in simplest exact form.

Worked example

Simplify 3√72.

18√2.

Factor 72 as 36 × 2. Since √36 = 6, the expression becomes 3 × 6√2 = 18√2.

Teaching notes

Make the practice count

  • Look for the largest square factor first.
  • Check whether a remaining radicand still contains a square factor.
  • Distinguish exact radical form from a decimal approximation.
  • Use the square roots chart if square recognition needs support.

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Configured PDF · Simplify Square Roots · US Letter

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Math SheetNameScore/ 10TeacherDateSimplify Square RootsExtract the greatest square factor.1.252.3843.2·1124.495.206.2·207.648.2509.3·44810.4math-sheet.comPage 1 / 1

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