Rationalize the Denominator Calculator

About this calculator

Rationalizing the denominator means rewriting a fraction like a/√b so that no square root remains on the bottom, by multiplying both the numerator and denominator by √b. Since √b × √b = b, the denominator becomes the rational number b, and the fraction becomes a√b / b — mathematically identical to the original, just written in a different, standardized form.

The convention exists because a rationalized denominator is easier to compare, add, and simplify: two fractions with irrational denominators are hard to combine directly, but once both have been rationalized, combining them is ordinary fraction arithmetic. It is a staple of algebra and pre-calculus courses, where students are expected to leave radical answers in rationalized form, and it also matters historically — before calculators, dividing by a rational number by hand was far easier than dividing by an irrational decimal approximation.

Enter a numerator a and a radicand b, and the calculator rationalizes a/√b, showing the simplified radical form and its decimal value.