Algebra 1 radical inequalities worksheet

Q: Are these radical inequalities worksheets free?

Yes. Every radical inequalities 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.

Q: Do the radical inequalities worksheets come with an answer key?

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.

Q: Are these radical inequalities worksheets printable?

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.

Q: What grade are these radical inequalities worksheets for?

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.

Q: Can I get a different version of the same radical inequalities worksheet?

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.

Q: Is this a free alternative to Kuta Software for radical inequalities?

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 inequalities 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.

Q: Can I choose how hard the radical inequalities questions are?

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.

Q: What do students get wrong with radical inequalities?

Forgetting the lower end. x < 22 alone lets in x = -10, where the root does not exist.

Square both sides as for an equation, then add the condition the root brings with it: whatever is under it cannot be negative. For "less than" that condition is the lower end of the answer; for "greater than or equal" it is already satisfied.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Radical Inequalities Date Period Solve each inequality. $\sqrt{3 x + 82} \geq 11$ $\sqrt{4 x + 69} \geq 11$ $\sqrt{2 x + 91} < 11$ $\sqrt{x + 86} < 10$ $\sqrt{2 x + 95} \geq 11$ $\sqrt{2 x + 74} < 10$ $\sqrt{3 x + 55} < 10$ $\sqrt{3 x + 102} < 12$ $\sqrt{3 x + 102} \geq 12$ $\sqrt{x + 85} < 10$ $\sqrt{2 x + 74} \geq 10$ $\sqrt{3 x + 61} < 10$ $\sqrt{3 x + 55} \geq 10$ $\sqrt{3 x + 58} \geq 10$ $\sqrt{4 x + 84} \geq 12$ $\sqrt{4 x + 40} < 10$ $\sqrt{4 x + 92} \geq 12$ $\sqrt{4 x + 40} \geq 10$ $\sqrt{4 x + 92} < 12$ $\sqrt{2 x + 95} < 11$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Radical Inequalities

Date Period

Solve each inequality.

$\sqrt{3 x + 82} \geq 11$
$\sqrt{4 x + 69} \geq 11$
$\sqrt{2 x + 91} < 11$
$\sqrt{x + 86} < 10$
$\sqrt{2 x + 95} \geq 11$
$\sqrt{2 x + 74} < 10$
$\sqrt{3 x + 55} < 10$
$\sqrt{3 x + 102} < 12$
$\sqrt{3 x + 102} \geq 12$
$\sqrt{x + 85} < 10$
$\sqrt{2 x + 74} \geq 10$
$\sqrt{3 x + 61} < 10$
$\sqrt{3 x + 55} \geq 10$
$\sqrt{3 x + 58} \geq 10$
$\sqrt{4 x + 84} \geq 12$
$\sqrt{4 x + 40} < 10$
$\sqrt{4 x + 92} \geq 12$
$\sqrt{4 x + 40} \geq 10$
$\sqrt{4 x + 92} < 12$
$\sqrt{2 x + 95} < 11$



Sigma Prep · sigmaprep.io/worksheets Name Radical InequalitiesAnswer keyVersion 1 Date Period Solve each inequality. $\sqrt{3 x + 82} \geq 11$ $x \geq 13$ $\sqrt{4 x + 69} \geq 11$ $x \geq 13$ $\sqrt{2 x + 91} < 11$ $- \frac{91}{2} \leq x < 15$ $\sqrt{x + 86} < 10$ $- 86 \leq x < 14$ $\sqrt{2 x + 95} \geq 11$ $x \geq 13$ $\sqrt{2 x + 74} < 10$ $- 37 \leq x < 13$ $\sqrt{3 x + 55} < 10$ $- \frac{55}{3} \leq x < 15$ $\sqrt{3 x + 102} < 12$ $- 34 \leq x < 14$ $\sqrt{3 x + 102} \geq 12$ $x \geq 14$ $\sqrt{x + 85} < 10$ $- 85 \leq x < 15$ $\sqrt{2 x + 74} \geq 10$ $x \geq 13$ $\sqrt{3 x + 61} < 10$ $- \frac{61}{3} \leq x < 13$ $\sqrt{3 x + 55} \geq 10$ $x \geq 15$ $\sqrt{3 x + 58} \geq 10$ $x \geq 14$ $\sqrt{4 x + 84} \geq 12$ $x \geq 15$ $\sqrt{4 x + 40} < 10$ $- 10 \leq x < 15$ $\sqrt{4 x + 92} \geq 12$ $x \geq 13$ $\sqrt{4 x + 40} \geq 10$ $x \geq 15$ $\sqrt{4 x + 92} < 12$ $- 23 \leq x < 13$ $\sqrt{2 x + 95} < 11$ $- \frac{95}{2} \leq x < 13$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Radical InequalitiesAnswer keyVersion 1

Date Period

Solve each inequality.

$\sqrt{3 x + 82} \geq 11$ $x \geq 13$
$\sqrt{4 x + 69} \geq 11$ $x \geq 13$
$\sqrt{2 x + 91} < 11$ $- \frac{91}{2} \leq x < 15$
$\sqrt{x + 86} < 10$ $- 86 \leq x < 14$
$\sqrt{2 x + 95} \geq 11$ $x \geq 13$
$\sqrt{2 x + 74} < 10$ $- 37 \leq x < 13$
$\sqrt{3 x + 55} < 10$ $- \frac{55}{3} \leq x < 15$
$\sqrt{3 x + 102} < 12$ $- 34 \leq x < 14$
$\sqrt{3 x + 102} \geq 12$ $x \geq 14$
$\sqrt{x + 85} < 10$ $- 85 \leq x < 15$
$\sqrt{2 x + 74} \geq 10$ $x \geq 13$
$\sqrt{3 x + 61} < 10$ $- \frac{61}{3} \leq x < 13$
$\sqrt{3 x + 55} \geq 10$ $x \geq 15$
$\sqrt{3 x + 58} \geq 10$ $x \geq 14$
$\sqrt{4 x + 84} \geq 12$ $x \geq 15$
$\sqrt{4 x + 40} < 10$ $- 10 \leq x < 15$
$\sqrt{4 x + 92} \geq 12$ $x \geq 13$
$\sqrt{4 x + 40} \geq 10$ $x \geq 15$
$\sqrt{4 x + 92} < 12$ $- 23 \leq x < 13$
$\sqrt{2 x + 95} < 11$ $- \frac{95}{2} \leq x < 13$

How to do these

$\sqrt{x + 3} < 5$

Square: x + 3 < 25, so x < 22.
Under the root: x + 3 ≥ 0, so x ≥ -3.

The answer is $- 3 \leq x < 22$ .

Where students go wrong

Forgetting the lower end. x < 22 alone lets in x = -10, where the root does not exist.

Also called square root inequalities, solving radical inequalities or inequalities with radicals.

Questions about these worksheets