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Exponents and radicals practice

Multiplying radical expressions worksheets

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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Multiply every required pair of terms, simplify the radicals and combine like terms. Use the positive-variable domain printed on variable problems.

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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.

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Learning objective

What this activity builds

Distribute radical products, simplify each resulting term and combine like radical parts.

Worked example

Expand and simplify (√3 + 2)(√3 − 1).

1 + √3.

The four products are 3, −√3, 2√3 and −2. Combine the rational terms and the matching radical terms.

Teaching notes

Make the practice count

  • Draw a small product grid for two binomials.
  • Keep all products visible before combining.
  • Multiply coefficients separately from radicands.
  • Check the stated variable domain before applying root product rules.

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Math SheetNameScore/ 10TeacherDateMultiply Radical ExpressionsMultiply and distribute radical expressions.1.6·5·22.3·5·x·1+3·5·xDomain: variables are positivex03.1+2·3·1+5·34.4·3·x·2·xDomain: variables are positivex05.6·4+66.2+5·x·2+5·xDomain: variables are positivex07.2·2·38.5·7·x·1+2·7·xDomain: variables are positivex09.1+6·7·1+3·710.2·7·x·5·xDomain: variables are positivex0math-sheet.comPage 1 / 1

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