Algebra 2 radical equations have a variable on both sides, two square roots set equal, or a cube root. Squaring often leads to a quadratic, and one of its roots can be extraneous, so the solution set comes from checking each one in the original.
Also taught in Algebra 1, at its own level and with its own examples.
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.
Square both sides: x + 7 = x² - 10x + 25, so x² - 11x + 18 = 0.
Factor: (x - 2)(x - 9) = 0, so x = 2 or x = 9.
Check: x = 2 gives 3 = -3, which fails; x = 9 gives 4 = 4.
The answer is {9}.
Where students go wrong
Squaring the right side as x² + 25. (x - 5)² is x² - 10x + 25, and dropping the middle term gives the wrong quadratic.
Also called square root equations or solving equations with radicals.
What you can put on this worksheet
A square root equation
v+42=7→ {7}
Cube roots, two radicals, extraneous roots
4x−18=x+3→ {7}
A fraction under the root, a variable beside it, two roots
m=−8+28+m→ {−3}
A number times the root, and the root of kx equal to x
−5r+1=−10→ {3}
Questions about these worksheets
Yes. Every radical 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 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 radical 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 4: a square root equation, cube roots, two radicals, extraneous roots, a fraction under the root, a variable beside it, two roots and a number times the root, and the root of kx equal to x. Tick as many as you want and set how many of each, or let it spread them evenly.
Not checking at the end. Squaring can invent solutions that fail in the original equation, so every answer has to go back in before it counts.