Dividing radicals worksheet for Algebra 1

A radical in the denominator is never a finished answer. Multiplying top and bottom by that radical clears it, and on the harder level the bottom is a binomial and needs its conjugate.

Also taught in Algebra 2, 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.



Sigma Prep · sigmaprep.io/worksheets Name Dividing Radicals Date Period Simplify. If a variable appears, assume it is positive. $\frac{7}{\sqrt{10}}$ $\frac{7 \sqrt{11}}{5 \sqrt{22}}$ $\frac{2}{\sqrt{6}}$ $\frac{3}{2 \sqrt{17}}$ $\frac{11}{\sqrt{11}}$ $\frac{\sqrt{10}}{\sqrt{7}}$ $\frac{3}{\sqrt{2}}$ $\frac{9 \sqrt{6}}{\sqrt{15}}$ $\frac{12}{\sqrt{3}}$ $\frac{8}{3 \sqrt{5}}$ $\frac{12}{\sqrt{10}}$ $\frac{\sqrt{3}}{\sqrt{14}}$ $\frac{117}{\sqrt{13}}$ $\frac{6 \sqrt{2}}{2 \sqrt{19}}$ $\frac{12}{\sqrt{11}}$ $\frac{\sqrt{7}}{\sqrt{21}}$ $\frac{4}{\sqrt{6}}$ $\frac{1}{5 \sqrt{13}}$ $\frac{14}{\sqrt{2}}$ $\frac{3 \sqrt{3}}{\sqrt{17}}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Dividing Radicals

Date Period

Simplify. If a variable appears, assume it is positive.

$\frac{7}{\sqrt{10}}$
$\frac{7 \sqrt{11}}{5 \sqrt{22}}$
$\frac{2}{\sqrt{6}}$
$\frac{3}{2 \sqrt{17}}$
$\frac{11}{\sqrt{11}}$
$\frac{\sqrt{10}}{\sqrt{7}}$
$\frac{3}{\sqrt{2}}$
$\frac{9 \sqrt{6}}{\sqrt{15}}$
$\frac{12}{\sqrt{3}}$
$\frac{8}{3 \sqrt{5}}$
$\frac{12}{\sqrt{10}}$
$\frac{\sqrt{3}}{\sqrt{14}}$
$\frac{117}{\sqrt{13}}$
$\frac{6 \sqrt{2}}{2 \sqrt{19}}$
$\frac{12}{\sqrt{11}}$
$\frac{\sqrt{7}}{\sqrt{21}}$
$\frac{4}{\sqrt{6}}$
$\frac{1}{5 \sqrt{13}}$
$\frac{14}{\sqrt{2}}$
$\frac{3 \sqrt{3}}{\sqrt{17}}$



Sigma Prep · sigmaprep.io/worksheets Name Dividing RadicalsAnswer keyVersion 1 Date Period Simplify. If a variable appears, assume it is positive. $\frac{7}{\sqrt{10}}$ $\frac{7 \sqrt{10}}{10}$ $\frac{7 \sqrt{11}}{5 \sqrt{22}}$ $\frac{7 \sqrt{2}}{10}$ $\frac{2}{\sqrt{6}}$ $\frac{\sqrt{6}}{3}$ $\frac{3}{2 \sqrt{17}}$ $\frac{3 \sqrt{17}}{34}$ $\frac{11}{\sqrt{11}}$ $\sqrt{11}$ $\frac{\sqrt{10}}{\sqrt{7}}$ $\frac{\sqrt{70}}{7}$ $\frac{3}{\sqrt{2}}$ $\frac{3 \sqrt{2}}{2}$ $\frac{9 \sqrt{6}}{\sqrt{15}}$ $\frac{9 \sqrt{10}}{5}$ $\frac{12}{\sqrt{3}}$ $4 \sqrt{3}$ $\frac{8}{3 \sqrt{5}}$ $\frac{8 \sqrt{5}}{15}$ $\frac{12}{\sqrt{10}}$ $\frac{6 \sqrt{10}}{5}$ $\frac{\sqrt{3}}{\sqrt{14}}$ $\frac{\sqrt{42}}{14}$ $\frac{117}{\sqrt{13}}$ $9 \sqrt{13}$ $\frac{6 \sqrt{2}}{2 \sqrt{19}}$ $\frac{3 \sqrt{38}}{19}$ $\frac{12}{\sqrt{11}}$ $\frac{12 \sqrt{11}}{11}$ $\frac{\sqrt{7}}{\sqrt{21}}$ $\frac{\sqrt{3}}{3}$ $\frac{4}{\sqrt{6}}$ $\frac{2 \sqrt{6}}{3}$ $\frac{1}{5 \sqrt{13}}$ $\frac{\sqrt{13}}{65}$ $\frac{14}{\sqrt{2}}$ $7 \sqrt{2}$ $\frac{3 \sqrt{3}}{\sqrt{17}}$ $\frac{3 \sqrt{51}}{17}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Dividing RadicalsAnswer keyVersion 1

Date Period

Simplify. If a variable appears, assume it is positive.

$\frac{7}{\sqrt{10}}$ $\frac{7 \sqrt{10}}{10}$
$\frac{7 \sqrt{11}}{5 \sqrt{22}}$ $\frac{7 \sqrt{2}}{10}$
$\frac{2}{\sqrt{6}}$ $\frac{\sqrt{6}}{3}$
$\frac{3}{2 \sqrt{17}}$ $\frac{3 \sqrt{17}}{34}$
$\frac{11}{\sqrt{11}}$ $\sqrt{11}$
$\frac{\sqrt{10}}{\sqrt{7}}$ $\frac{\sqrt{70}}{7}$
$\frac{3}{\sqrt{2}}$ $\frac{3 \sqrt{2}}{2}$
$\frac{9 \sqrt{6}}{\sqrt{15}}$ $\frac{9 \sqrt{10}}{5}$
$\frac{12}{\sqrt{3}}$ $4 \sqrt{3}$
$\frac{8}{3 \sqrt{5}}$ $\frac{8 \sqrt{5}}{15}$
$\frac{12}{\sqrt{10}}$ $\frac{6 \sqrt{10}}{5}$
$\frac{\sqrt{3}}{\sqrt{14}}$ $\frac{\sqrt{42}}{14}$
$\frac{117}{\sqrt{13}}$ $9 \sqrt{13}$
$\frac{6 \sqrt{2}}{2 \sqrt{19}}$ $\frac{3 \sqrt{38}}{19}$
$\frac{12}{\sqrt{11}}$ $\frac{12 \sqrt{11}}{11}$
$\frac{\sqrt{7}}{\sqrt{21}}$ $\frac{\sqrt{3}}{3}$
$\frac{4}{\sqrt{6}}$ $\frac{2 \sqrt{6}}{3}$
$\frac{1}{5 \sqrt{13}}$ $\frac{\sqrt{13}}{65}$
$\frac{14}{\sqrt{2}}$ $7 \sqrt{2}$
$\frac{3 \sqrt{3}}{\sqrt{17}}$ $\frac{3 \sqrt{51}}{17}$

How to do these

$\frac{6}{\sqrt{3}}$

Multiply top and bottom by root 3.
The bottom becomes 3.
6 root 3 over 3.

The answer is $2 \sqrt{3}$ .

Where students go wrong

Multiplying only the bottom. Both parts of the fraction have to be multiplied or the value changes, and the answer will be off by exactly the factor you forgot.

Also called dividing radicals, dividing square roots or quotient of radicals.

What you can put on this worksheet

Dividing, with the root cleared from the bottom: $\frac{9}{\sqrt{7}}$ → $\frac{9 \sqrt{7}}{7}$
A root over a root, and a binomial over a root: $\frac{12 \sqrt{30}}{3 \sqrt{6}}$ → $4 \sqrt{5}$
Numbers in front of the roots: $\frac{4 \sqrt{3}}{4 \sqrt{6}}$ → $\frac{\sqrt{2}}{2}$
Binomial denominators and cube or fourth roots: Simplify:
$\frac{\sqrt[3]{2}}{\sqrt[3]{9}}$ → $\frac{\sqrt[3]{6}}{3}$
Letters under the roots, a sum on top, two roots on the bottom: $\frac{- 5 + 2 \sqrt{6}}{5 \sqrt{5}}$ → $\frac{2 \sqrt{30} - 5 \sqrt{5}}{25}$

Questions about these worksheets

Yes. Every dividing 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 dividing 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 two 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 5: dividing, with the root cleared from the bottom, a root over a root, and a binomial over a root, numbers in front of the roots, binomial denominators and cube or fourth roots and letters under the roots, a sum on top, two roots on the bottom. Tick as many as you want and set how many of each, or let it spread them evenly.

Multiplying only the bottom. Both parts of the fraction have to be multiplied or the value changes, and the answer will be off by exactly the factor you forgot.

Dividing radicals worksheet for Algebra 1

Select your difficulty

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these dividing radicals worksheets free?+

Do the dividing radicals worksheets come with an answer key?+

Are these dividing radicals worksheets printable?+

What grade are these dividing radicals worksheets for?+

Can I get a different version of the same dividing radicals worksheet?+

Is this a free alternative to Kuta Software for dividing radicals?+

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What do students get wrong with dividing radicals?+