Rationalize the Denominator Calculator
Enter a fraction with a square root in the denominator below to instantly get the rationalized form.
For numerator / √radicand
How to Rationalize a Denominator
Multiply the numerator and denominator by the same radical that's in the denominator: a/√b = (a × √b) / (√b × √b) = (a√b) / b.
Worked example
Rationalize 5/√3.
5/√3 × √3/√3 = 5√3 / 3
Result: 5√3 / 3
Frequently Asked Questions
Why do you rationalize a denominator?
By convention, a fraction shouldn't have a radical (square root) left in the denominator. Rationalizing rewrites it in an equivalent form with the radical only in the numerator.
How do you rationalize a single-term radical denominator?
Multiply the top and bottom by that same radical. Since √b × √b = b, the denominator becomes a whole number: a/√b = (a√b)/b.
Does rationalizing change the value of the fraction?
No. Multiplying by √b/√b is really multiplying by 1, since the radical divided by itself equals 1 — so the value stays exactly the same, only the form changes.
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