WebToolArcHow to use this Square Root of Fraction Calculator
Enter an integer numerator and non-zero denominator to reduce the fraction, simplify numerator and denominator radicals, and calculate a decimal value.
What it calculates
Calculate and simplify the square root of a fraction.
Browser limits
Exact integer radical factorization is capped at 1 trillion for responsive local processing. The long-division page supports up to 60 integer digits and 12 generated decimal places.
Exact roots and decimal approximations are different outputs
A square root is exact when the radicand can be expressed as a perfect square in the working number system. Otherwise the decimal expansion is generally nonterminating, so displayed digits are an approximation. For a fraction, numerator and denominator can be simplified before taking roots; rationalizing or radical simplification may preserve an exact form better than early decimal rounding.
Verify by squaring the result
Square an exact simplified result to recover the original value, or square the decimal approximation and compare within the expected rounding tolerance. The long-division method exposes how successive digit pairs produce additional decimal digits, but extra displayed digits do not create extra certainty beyond the chosen precision. Negative radicands require a complex-number interpretation rather than an ordinary real square root.