What this calculator does
Rationalize a denominator works out removes a square root from the denominator of a/(b + c√n) using the conjugate. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulaa/(b+c√n) × (b−c√n)/(b−c√n) = [a(b−c√n)] / (b²−c²n)
The inputs explained
| Field | What to enter |
|---|---|
| Numerator a | A number. Starts at 1. |
| Denominator constant term b | A number. Starts at 1. |
| Denominator root coefficient c | A number. Starts at 1. |
| Radicand n | A number. Starts at 2. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with numerator a
Every other input is held at the calculator’s starting values while numerator a varies. Select any row to load that scenario into the calculator.
How the answer changes with numerator a