Worksheets · Algebra 1

Solving quadratics by taking square roots worksheet

When the equation has a square on one side and a number on the other, there is no need to factor at all. You can also mix in equations with no real solution, which is where the negative on the right actually matters.

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

Solving Quadratics by Square Roots

Date Period

Solve each equation by taking square roots.

  1. (a−5)2=144
  2. (y−6)2=81
  3. (p+5)2=36
  4. (n−3)2=4
  5. (p−4)2=100
  6. (b−1)2=36
  7. (v+3)2=9
  8. (a+7)2=9
  9. (r−7)2=144
  10. (b+2)2=16
  11. (p−2)2=81
  12. (v−3)2=1
  13. (a+3)2=144
  14. (r−3)2=81
  15. (y+7)2=144
  16. (k+2)2=1
  17. (k−8)2=49
  18. (y+2)2=81
  19. (y−9)2=4
  20. (m−4)2=16

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

Sigma Prep · sigmaprep.io/worksheets

Name

Solving Quadratics by Square RootsAnswer keyVersion 1

Date Period

Solve each equation by taking square roots.

  1. (a−5)2=144{17,−7}
  2. (y−6)2=81{15,−3}
  3. (p+5)2=36{1,−11}
  4. (n−3)2=4{5,1}
  5. (p−4)2=100{14,−6}
  6. (b−1)2=36{7,−5}
  7. (v+3)2=9{0,−6}
  8. (a+7)2=9{−4,−10}
  9. (r−7)2=144{19,−5}
  10. (b+2)2=16{2,−6}
  11. (p−2)2=81{11,−7}
  12. (v−3)2=1{4,2}
  13. (a+3)2=144{9,−15}
  14. (r−3)2=81{12,−6}
  15. (y+7)2=144{5,−19}
  16. (k+2)2=1{−1,−3}
  17. (k−8)2=49{15,1}
  18. (y+2)2=81{7,−11}
  19. (y−9)2=4{11,7}
  20. (m−4)2=16{8,0}

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

How to do these

(x−3)2=16

  1. Take the square root of both sides.
  2. A square root gives two answers: x - 3 = 4 or x - 3 = -4.
  3. So x = 7 or x = -1.

The answer is x=7 or x=−1.

Where students go wrong

Writing only the positive root. (x - 3)² = 16 has two answers, and a student who takes only the 4 loses half the solution every time. The other one is a negative on the right: (x - 3)² = -16 has no real answer at all, because nothing real squares to a negative.

Also called the square root property or the square root method.

What you can put on this worksheet

A square equal to a number
v2=49 → {7,−7}
Mix in some with no real solution
v2=−23 → No solution

Questions about these worksheets

Yes. Every solving quadratics by taking square 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 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 solving quadratics by taking square 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: a square equal to a number and mix in some with no real solution. Tick as many as you want and set how many of each, or let it spread them evenly.

Writing only the positive root. (x - 3)² = 16 has two answers, and a student who takes only the 4 loses half the solution every time. The other one is a negative on the right: (x - 3)² = -16 has no real answer at all, because nothing real squares to a negative.