Adding and subtracting radicals worksheet

Radicals add exactly like terms do: only when what is under the root already matches. The harder levels hide the match until each one is simplified.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Adding and Subtracting Radicals Date Period Simplify. $- 8 \sqrt{117} + 9 \sqrt{208}$ $- 9 \sqrt{56} - 8 \sqrt{126}$ $- 8 \sqrt{125} - 8 \sqrt{45}$ $- 8 \sqrt{45} + 9 \sqrt{20}$ $9 \sqrt{117} - 9 \sqrt{325}$ $- 9 \sqrt{171} - 7 \sqrt{76}$ $8 \sqrt{12} - 7 \sqrt{48}$ $- 9 \sqrt{153} + 8 \sqrt{272}$ $9 \sqrt{475} + 9 \sqrt{76}$ $7 \sqrt{50} + 8 \sqrt{32}$ $9 \sqrt{12} - 9 \sqrt{27}$ $- 7 \sqrt{48} + 8 \sqrt{12}$ $7 \sqrt{375} - 7 \sqrt{135}$ $8 \sqrt{12} - 7 \sqrt{27}$ $7 \sqrt{56} + 8 \sqrt{350}$ $9 \sqrt{24} + 7 \sqrt{150}$ $9 \sqrt{150} - 7 \sqrt{24}$ $- 8 \sqrt{75} + 7 \sqrt{27}$ $8 \sqrt{153} + 7 \sqrt{68}$ $9 \sqrt{24} - 7 \sqrt{150}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Adding and Subtracting Radicals

Date Period

Simplify.

$- 8 \sqrt{117} + 9 \sqrt{208}$
$- 9 \sqrt{56} - 8 \sqrt{126}$
$- 8 \sqrt{125} - 8 \sqrt{45}$
$- 8 \sqrt{45} + 9 \sqrt{20}$
$9 \sqrt{117} - 9 \sqrt{325}$
$- 9 \sqrt{171} - 7 \sqrt{76}$
$8 \sqrt{12} - 7 \sqrt{48}$
$- 9 \sqrt{153} + 8 \sqrt{272}$
$9 \sqrt{475} + 9 \sqrt{76}$
$7 \sqrt{50} + 8 \sqrt{32}$
$9 \sqrt{12} - 9 \sqrt{27}$
$- 7 \sqrt{48} + 8 \sqrt{12}$
$7 \sqrt{375} - 7 \sqrt{135}$
$8 \sqrt{12} - 7 \sqrt{27}$
$7 \sqrt{56} + 8 \sqrt{350}$
$9 \sqrt{24} + 7 \sqrt{150}$
$9 \sqrt{150} - 7 \sqrt{24}$
$- 8 \sqrt{75} + 7 \sqrt{27}$
$8 \sqrt{153} + 7 \sqrt{68}$
$9 \sqrt{24} - 7 \sqrt{150}$



Sigma Prep · sigmaprep.io/worksheets Name Adding and Subtracting RadicalsAnswer keyVersion 1 Date Period Simplify. $- 8 \sqrt{117} + 9 \sqrt{208}$ $12 \sqrt{13}$ $- 9 \sqrt{56} - 8 \sqrt{126}$ $- 42 \sqrt{14}$ $- 8 \sqrt{125} - 8 \sqrt{45}$ $- 64 \sqrt{5}$ $- 8 \sqrt{45} + 9 \sqrt{20}$ $- 6 \sqrt{5}$ $9 \sqrt{117} - 9 \sqrt{325}$ $- 18 \sqrt{13}$ $- 9 \sqrt{171} - 7 \sqrt{76}$ $- 41 \sqrt{19}$ $8 \sqrt{12} - 7 \sqrt{48}$ $- 12 \sqrt{3}$ $- 9 \sqrt{153} + 8 \sqrt{272}$ $5 \sqrt{17}$ $9 \sqrt{475} + 9 \sqrt{76}$ $63 \sqrt{19}$ $7 \sqrt{50} + 8 \sqrt{32}$ $67 \sqrt{2}$ $9 \sqrt{12} - 9 \sqrt{27}$ $- 9 \sqrt{3}$ $- 7 \sqrt{48} + 8 \sqrt{12}$ $- 12 \sqrt{3}$ $7 \sqrt{375} - 7 \sqrt{135}$ $14 \sqrt{15}$ $8 \sqrt{12} - 7 \sqrt{27}$ $- 5 \sqrt{3}$ $7 \sqrt{56} + 8 \sqrt{350}$ $54 \sqrt{14}$ $9 \sqrt{24} + 7 \sqrt{150}$ $53 \sqrt{6}$ $9 \sqrt{150} - 7 \sqrt{24}$ $31 \sqrt{6}$ $- 8 \sqrt{75} + 7 \sqrt{27}$ $- 19 \sqrt{3}$ $8 \sqrt{153} + 7 \sqrt{68}$ $38 \sqrt{17}$ $9 \sqrt{24} - 7 \sqrt{150}$ $- 17 \sqrt{6}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Adding and Subtracting RadicalsAnswer keyVersion 1

Date Period

Simplify.

$- 8 \sqrt{117} + 9 \sqrt{208}$ $12 \sqrt{13}$
$- 9 \sqrt{56} - 8 \sqrt{126}$ $- 42 \sqrt{14}$
$- 8 \sqrt{125} - 8 \sqrt{45}$ $- 64 \sqrt{5}$
$- 8 \sqrt{45} + 9 \sqrt{20}$ $- 6 \sqrt{5}$
$9 \sqrt{117} - 9 \sqrt{325}$ $- 18 \sqrt{13}$
$- 9 \sqrt{171} - 7 \sqrt{76}$ $- 41 \sqrt{19}$
$8 \sqrt{12} - 7 \sqrt{48}$ $- 12 \sqrt{3}$
$- 9 \sqrt{153} + 8 \sqrt{272}$ $5 \sqrt{17}$
$9 \sqrt{475} + 9 \sqrt{76}$ $63 \sqrt{19}$
$7 \sqrt{50} + 8 \sqrt{32}$ $67 \sqrt{2}$
$9 \sqrt{12} - 9 \sqrt{27}$ $- 9 \sqrt{3}$
$- 7 \sqrt{48} + 8 \sqrt{12}$ $- 12 \sqrt{3}$
$7 \sqrt{375} - 7 \sqrt{135}$ $14 \sqrt{15}$
$8 \sqrt{12} - 7 \sqrt{27}$ $- 5 \sqrt{3}$
$7 \sqrt{56} + 8 \sqrt{350}$ $54 \sqrt{14}$
$9 \sqrt{24} + 7 \sqrt{150}$ $53 \sqrt{6}$
$9 \sqrt{150} - 7 \sqrt{24}$ $31 \sqrt{6}$
$- 8 \sqrt{75} + 7 \sqrt{27}$ $- 19 \sqrt{3}$
$8 \sqrt{153} + 7 \sqrt{68}$ $38 \sqrt{17}$
$9 \sqrt{24} - 7 \sqrt{150}$ $- 17 \sqrt{6}$

How to do these

$\sqrt{8} + \sqrt{18}$

Neither is simplified yet, so they look unlike.
8 is 4 times 2 and 18 is 9 times 2.
2 root 2 plus 3 root 2.

The answer is $5 \sqrt{2}$ .

Where students go wrong

Adding what is under the roots. Root 8 plus root 18 is not root 26. Simplify first, and only add when the insides already agree.

Also called adding surds, combining radicals or like radicals.

Questions about these worksheets

Yes. Every adding and subtracting radicals 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 adding and subtracting radicals 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.

Adding what is under the roots. Root 8 plus root 18 is not root 26. Simplify first, and only add when the insides already agree.

Adding and subtracting radicals worksheet

Select your difficulty

Adding and Subtracting Radicals

Adding and Subtracting RadicalsAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

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