Rationalise the Denominator Calculator

This calculator rationalises a fraction of the form a over root b, removing the square root from the denominator so the expression is easier to work with, add or compare. You enter the numerator, a, and the number under the root, b, and the calculator multiplies the top and bottom by root b, which turns the denominator into a whole number, then simplifies the surd and cancels any common factor between the numerator and denominator. The result card shows the simplified fraction in the form a over root b, the decimal value of the original expression so you can check the rationalised version matches, and the simplified radicand left under the root. This matters because a surd sitting in the denominator is awkward in algebra: it is harder to add fractions with different surd denominators, harder to compare sizes, and harder to spot when two expressions are actually equal. Rationalising fixes that without changing the value, since you are effectively multiplying by a form of 1. Use it to check homework, confirm a simplification step, or convert a surd expression into the tidy form usually expected in algebra and calculus courses. Try entering 1 and 2 to see 1 over root 2 become root 2 over 2, about 0.707107, then try 2 and 8 to see the same simplified answer appear from a different starting fraction.

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