Rationalize the Denominator Calculator

How it is calculated

For a / √b the tool multiplies top and bottom by √b: a / √b = a√b / b, because √b × √b = b. The first output prints exactly that, with b as originally typed, and it does not cancel the fraction (6√3 / 3 is not reduced to 2√3). The second output is the root √b alone, simplified by pulling out the largest square factor: √b = k√m where k² is the biggest perfect square dividing b. The decimal output is a ÷ √b to four places, calculated from the exact numerator. The numerator may be any number, including a decimal or negative one, and in the first line it is printed with up to four decimals (trailing zeros dropped), so 2.567 appears as 2.567 and 2.50 as 2.5. The radicand must be a positive whole number up to one trillion, so 0, negatives, values like 2.5 and larger numbers give no result.

Common mistakes

• Expecting the first output to be fully reduced: it keeps b as typed, so you still have to cancel common factors yourself, as 6√3 / 3 = 2√3.
• Reading the simplified-radical line as the whole answer: it is only √b simplified (for example 2√3), and the numerator a and the denominator are not included.
• Entering the radicand as a decimal such as 2.5, or a negative number: only positive whole numbers work, and anything else gives no result.
• Putting the whole denominator in the radicand when it is something like 3 + √2: this tool handles only a single square root a/√b, not a binomial denominator.
• Treating a perfect square, for example b = 16, as irrational: the radical comes back as the plain whole number 4, and no square root remains.