🔢 Rationalizing the Denominator Calculator
Enter a fraction of the form a ÷ (b·√c) to rationalize the denominator and remove the square root from the bottom.
What does rationalizing the denominator mean?
Rationalizing the denominator means rewriting a fraction so that no square root (or other radical) remains in the bottom of the fraction, without changing the fraction’s value.
How this calculator works
For a fraction of the form a ÷ (b·√c), multiplying both the numerator and denominator by √c removes the radical from the denominator, since √c × √c = c. This gives the rationalized form (a·√c) ÷ (b·c), which this calculator then reduces to lowest terms when the numbers involved are whole numbers.
For denominators with two terms (like 1 ÷ (√2 + 1)), the standard technique instead multiplies by the conjugate of the denominator; that case isn’t covered by this simplified single-term tool.
This calculator is for general educational and reference purposes.