Worksheets · Algebra 2

Algebra 2 multiplying radicals worksheet

Multiplying is the easy direction: the insides multiply whether they match or not. The work is all in simplifying what comes out.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multiplying Radicals

Date Period

Simplify. Assume all variables are positive.

  1. 414⋅72
  2. (3+7)(3−7)
  3. 717⋅410
  4. (3+2)(2−2)
  5. 5⋅311
  6. (5+3)(5−3)
  7. 52⋅610
  8. 3(7+5)
  9. 45⋅617
  10. (3+10)(3−10)
  11. 35⋅27
  12. 10(6−2)
  13. 72⋅214
  14. (10+5)(10−5)
  15. 77⋅715
  16. (11+10)(11−10)
  17. 22⋅73
  18. 11(6+5)
  19. 75⋅15
  20. (3+6)(3−6)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multiplying RadicalsAnswer keyVersion 1

Date Period

Simplify. Assume all variables are positive.

  1. 414⋅72567
  2. (3+7)(3−7)−4
  3. 717⋅41028170
  4. (3+2)(2−2)−2+4
  5. 5⋅311355
  6. (5+3)(5−3)2
  7. 52⋅610605
  8. 3(7+5)53+21
  9. 45⋅6172485
  10. (3+10)(3−10)−7
  11. 35⋅27635
  12. 10(6−2)−210+215
  13. 72⋅214287
  14. (10+5)(10−5)5
  15. 77⋅71549105
  16. (11+10)(11−10)1
  17. 22⋅73766
  18. 11(6+5)511+66
  19. 75⋅15353
  20. (3+6)(3−6)−3

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

6⋅10

  1. Multiply the insides: 60.
  2. 60 has a factor of 4.

The answer is 215.

Where students go wrong

Leaving the answer as root 60. Multiplying almost always produces a square factor, so the last step is checking whether anything can come out.

Also called multiplying radicals or products of radicals.

What you can put on this worksheet

Multiplying
7⋅7 → 7
Distributing, and multiplying binomials
6(10−3) → −36+215
Negative factors, and a root times a sum
314⋅(−43) → −1242
Numbers on the roots, two different roots, letters under the root
12a2⋅−22a3 → −4a26a

Questions about these worksheets

Yes. Every multiplying radicals sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the multiplying radicals questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: multiplying, distributing, and multiplying binomials, negative factors, and a root times a sum and numbers on the roots, two different roots, letters under the root. Tick as many as you want and set how many of each, or let it spread them evenly.

Leaving the answer as root 60. Multiplying almost always produces a square factor, so the last step is checking whether anything can come out.