Rationalize a denominator containing a square root and see the exact result written in a cleaner form.
Last updated: June 2026 | By Patchworkr Team
Rationalizing the denominator means rewriting a fraction so the denominator no longer contains a radical. For a simple form like 1 / sqrt(n), multiply numerator and denominator by sqrt(n).
That turns the denominator into an integer while keeping the value of the expression unchanged.
For 3 / sqrt(5), the rationalized form is 3 sqrt(5) / 5.
No. Multiplying by sqrt(n)/sqrt(n) is multiplying by 1, so the value stays the same.
No. The calculator requires a positive radicand for the square-root form used here.
Yes. If the numerator and denominator share a common factor, it reduces them.
This calculator is designed for whole-number inputs so the exact rationalized form stays clear.
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