Worksheets · Algebra 2

Simplifying nth roots worksheet

Look for factors that are perfect cubes (for a cube root) or perfect fourth powers (for a fourth root) and take them out. An odd root of a negative number is negative.

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

Simplifying Nth Roots

Date Period

Simplify. Assume every variable is positive.

  1. 8914
  2. 3−1523
  3. 59605
  4. −6405
  5. 3783
  6. 2−563
  7. 415364
  8. −24305
  9. 55943
  10. −4865
  11. 3684
  12. 3−3243
  13. 8965
  14. 4−18563
  15. 31284
  16. −3525
  17. 47685
  18. 1124
  19. −2563
  20. 2−883

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

Sigma Prep · sigmaprep.io/worksheets

Name

Simplifying Nth RootsAnswer keyVersion 1

Date Period

Simplify. Assume every variable is positive.

  1. 89143114
  2. 3−1523−6193
  3. 5960510305
  4. −6405−2205
  5. 37833143
  6. 2−563−473
  7. 4153641664
  8. −24305−3105
  9. 5594315223
  10. −4865−325
  11. 36842234
  12. 3−3243−9123
  13. 89652285
  14. 4−18563−16293
  15. 31284684
  16. −3525−2115
  17. 476858245
  18. 1124274
  19. −2563−443
  20. 2−883−4113

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

How to do these

543

  1. 54 = 27 × 2, and 27 is a perfect cube.
  2. The cube root of 27 is 3.

The answer is 323.

Where students go wrong

Pulling out perfect squares from a cube root. Under a cube root only perfect cubes come out: 8, 27, 64, 125.

Also called cube roots, fourth roots or higher-index radicals.

What you can put on this worksheet

Cube, fourth and fifth roots
22503 → 1023
Combine, multiply, variables and absolute values
Simplify: 216xy3 → 6y6xy

Questions about these worksheets

Yes. Every simplifying nth roots 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 simplifying nth roots 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 2: cube, fourth and fifth roots and combine, multiply, variables and absolute values. Tick as many as you want and set how many of each, or let it spread them evenly.

Pulling out perfect squares from a cube root. Under a cube root only perfect cubes come out: 8, 27, 64, 125.