Rationalize the Denominator Calculator

This page rationalises a denominator and shows the working. One action takes a fraction with a single square root underneath and multiplies top and bottom by that root; the other takes a sum or difference of two roots and multiplies by its conjugate, so the difference of two squares clears both at once. Each step is printed, the surviving root is reduced to simplest radical form, the fraction is put in lowest terms and a decimal is given so you can check the value never changed. Coefficients may be negative, and setting a radicand to 1 turns that term into a plain whole number.

Calculator Type

For a fraction shaped like a.sqrt(b) / (c.sqrt(d)). Multiply top and bottom by sqrt(d), then simplify what is left. Set a radicand to 1 for a term with no root.

Leave blank for 1. Negatives are allowed.
Use 1 when the top has no square root, so the top is just the number in front.
Cannot be zero.
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For a fraction shaped like p / (b.sqrt(m) + c.sqrt(n)). Multiplying by the conjugate turns the bottom into a difference of two squares and removes both roots at once. Set m to 1 when the first term is a plain number.

A whole number on top. Negatives are allowed.
Use 1 to make the first term a plain number, as in 3 + 2sqrt(5).
Negative for a minus sign between the two terms.
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