A simplified answer has no root in the denominator. With a single root on the bottom, multiply the top and bottom by that root. With a binomial like 3 + the square root of 2, multiply by its conjugate, 3 minus the square root of 2, so the roots cancel.
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.
Multiply the top and bottom by the square root of 3.
The bottom becomes 3.
6 times root 3 over 3 is 2 root 3.
The answer is 23.
Where students go wrong
Multiplying only the denominator by the root. The top has to be multiplied by the same thing, or the value changes.
Also called rationalizing the denominator, rationalizing denominators, conjugates or simplifying radical fractions.
What you can put on this worksheet
Dividing, with the root cleared from the bottom
742→ 67
A root over a root, and a binomial over a root
666→ 11
Numbers in front of the roots
4643→ 22
Binomial denominators and cube or fourth roots
Simplify: 3932→ 336
Questions about these worksheets
Yes. Every rationalizing the denominator 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 rationalizing the denominator 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: 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 and binomial denominators and cube or fourth roots. Tick as many as you want and set how many of each, or let it spread them evenly.
Multiplying only the denominator by the root. The top has to be multiplied by the same thing, or the value changes.