Exponents and radicals practice
Generate twelve dividing-radicals questions in independently selectable easy, medium and hard profiles, with exact rationalization, higher perfect roots and real-variable domain cases.
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Simplify each quotient exactly. Rationalize square-root denominators, preserve every original real-domain restriction, and use both printed cases when the conjugate norm can be zero.
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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.
Need the earlier eight-question edition? Download its student worksheet or download its worksheet with answers. Existing custom settings links also retain that edition until you change difficulty or reset.
Learning objective
Rewrite a radical quotient with a rational denominator while preserving equivalence on its original domain.
Worked example
√5 − 2.
Multiply both parts by √5 − 2. The denominator becomes (√5)² − 2² = 1, leaving √5 − 2.
Teaching notes
Make it yours
Choose your options, update the preview, then download the exact same pages.
Choose one or more difficulty profiles for twelve questions. Easy cycles through four answer outcomes, medium cycles through three rationalizing forms, and hard cycles through four source-backed families. Earlier settings links keep their original questions when paper, note, language or seed changes. Changing difficulty or Reset uses the current edition.
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