Worksheets · Algebra 1

Radical and rational equations worksheet

Two shapes that both need clearing before you can solve: square both sides to remove a root, multiply through to remove a denominator.

Select your difficulty

Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Radical and Rational Equations

Date Period

Solve each equation.

  1. 2a+122=12
  2. −110b−8=−18
  3. 4n−11−4=−1
  4. 15r+12=7
  5. 3b+22=8
  6. 70n−12=−2
  7. 3n−11+6=10
  8. −9n−15=−6
  9. 4r+53=9
  10. 130y−1=9
  11. 3k−5=7
  12. −20r+3=5
  13. 2m+7=5
  14. 18v−3=6
  15. 6m−27=3
  16. 2v−11=−12
  17. 2a+27+3=10
  18. −26y−15=−17
  19. 5m−81+8=11
  20. 10r+5=0

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

Sigma Prep · sigmaprep.io/worksheets

Name

Radical and Rational EquationsAnswer keyVersion 1

Date Period

Solve each equation.

  1. 2a+122=12{11}
  2. −110b−8=−18{11}
  3. 4n−11−4=−1{5}
  4. 15r+12=7{−3}
  5. 3b+22=8{14}
  6. 70n−12=−2{7}
  7. 3n−11+6=10{9}
  8. −9n−15=−6{−1}
  9. 4r+53=9{7}
  10. 130y−1=9{13}
  11. 3k−5=7{18}
  12. −20r+3=5{−10}
  13. 2m+7=5{9}
  14. 18v−3=6{2}
  15. 6m−27=3{6}
  16. 2v−11=−12{−2}
  17. 2a+27+3=10{11}
  18. −26y−15=−17{13}
  19. 5m−81+8=11{18}
  20. 10r+5=0{−2}

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

How to do these

3x+4=5

  1. Square both sides to get rid of the root.
  2. 3x + 4 = 25.
  3. Then solve as usual.

The answer is x=7.

Where students go wrong

Not checking the answer. Squaring both sides can invent solutions that do not work in the original equation, so every answer has to go back in. With a denominator the danger is the opposite: a value that makes the bottom zero has to be thrown out.

Also called square root equations or equations with fractions.

What you can put on this worksheet

A square root equation
v+42=7 → {7}
An equation with a variable underneath
30v=5 → {6}

Questions about these worksheets

Yes. Every radical and rational equations 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 1 is usually taken around 8th or 9th 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 radical and rational equations 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: a square root equation and an equation with a variable underneath. Tick as many as you want and set how many of each, or let it spread them evenly.

Not checking the answer. Squaring both sides can invent solutions that do not work in the original equation, so every answer has to go back in. With a denominator the danger is the opposite: a value that makes the bottom zero has to be thrown out.