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.
Preview and downloadExponents and radicals practice
Solving radical equations worksheets
Generate 10 radical equations in independently selectable Easy, Medium and Hard profiles. Practice isolating roots, solving, and rejecting candidates that fail the original equation.
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Solve for the variable, then substitute every candidate into the original equation. Keep only values that are real and make both sides equal.
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The original equation decides
A value is a solution only if the original expressions are real and the two sides are equal. Squaring both sides can introduce candidates that fail this final check.
A positive square equation has two opposite roots, while a principal square-root expression has one nonnegative value. Keep those two instructions distinct.
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.
Need the earlier solution-count edition? Download its student worksheet or download its worksheet with answers. Existing custom links retain that edition until you change Difficulty or reset.
Learning objective
What this activity builds
Solve a radical equation and verify each candidate against the original real-number domain and equality.
Worked example
Solve √(15 − 2x) = x.
x = 3.
Squaring gives x² + 2x − 15 = 0, with candidates 3 and −5. Substituting 3 gives 3 = 3. Substituting −5 gives 5 = −5, so −5 is extraneous.
Teaching notes
Make the practice count
- Write any sign or radicand restrictions before squaring.
- Keep a candidate list separate from the final solution set.
- Check the original equation, not only its squared form.
- Begin with Easy, then add Medium and Hard as learners are ready for more variable terms and possible extra candidates.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose any nonempty combination of Easy, Medium and Hard for ten questions. Easy uses one or two solving steps, Medium has exactly one valid root after checking, and Hard can have one or two valid roots. Earlier solution-count links keep their original questions until you change Difficulty or reset.
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A useful next step
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