Square Root Calculator: Compute Roots and Simplify Radicals Instantly
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 times 5 equals 25. Square roots are one of the most fundamental operations in mathematics, appearing in geometry, physics, engineering, statistics, and everyday problem-solving. Our calculator goes beyond simple square roots by also offering cube roots, nth roots, and radical simplification.
This calculator supports three root types. The square root (index 2) is the most common, used to find side lengths of squares given their area, or to compute distances using the Pythagorean theorem. The cube root (index 3) finds a number whose cube equals the input, essential for volume calculations. The nth root generalizes this concept to any positive integer index, enabling advanced mathematical and scientific computations.
One of the standout features is radical simplification. When you enter a number like 72, the calculator not only gives you the decimal approximation (8.485...) but also the simplified radical form: 6√2. This works by factoring out perfect square factors from under the radical sign. The tool also checks whether your input is a perfect square, meaning its square root is an exact integer with no remainder.
You can control decimal precision from 0 to 15 digits, making this suitable for both quick estimates and high-precision scientific work. The calculation history keeps your recent results for easy reference, and the copy button lets you transfer results to other applications. All calculations run entirely in your browser with zero server calls, ensuring privacy and instant results.