Simplify Radical Calculator

How the simplify radical calculator works

A square root is simplified by moving every complete square factor outside the radical. This calculator searches downward from the integer square root to find the largest factor whose square divides the input exactly. The square root of that factor becomes the outside multiplier, while the remaining quotient stays under the radical. The process preserves the original value without replacing it by a decimal approximation.

For the default input 72, the largest square factor is 36. Splitting the radicand gives the square root of 36 times 2, and the square root of 36 is 6. The verified simplified form is therefore 6 times the square root of 2. Squaring that expression gives 36 times 2, returning the original value 72.

Reading simplify radical calculator results privately

The input must be a nonnegative integer because the page performs exact divisibility checks. Negative radicands would require imaginary numbers, and fractional radicands need numerator-and-denominator simplification that is not represented here. A result with outside factor one is already square-free. Very large safe integers may take longer because the search checks possible square factors directly. This simplify radical calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.