Square Root Calculator

Square Root Calculator

Calculate square roots, cube roots, and nth roots of any number with precision up to six decimal places. This tool also computes the square and cube of your input and its reciprocal, making it a one-stop resource for students, engineers, and anyone working with exponents and radicals.

How Square Roots Are Calculated

The nth root of a number is computed using the formula: result = x^(1/n), where x is the input and n is the root degree. A square root uses n = 2, a cube root uses n = 3, and you can enter any custom root up to 100. The calculator also flags perfect squares — numbers whose square root is a whole integer (e.g., 144 = 12).

Example

Key Factors That Affect Root Calculations

• Perfect squares — numbers like 4, 9, 16, 25 yield clean whole-number square roots
• Negative inputs — even roots of negative numbers are undefined in real numbers; odd roots are valid (e.g., cube root of -8 = -2)
• Precision needs — results are rounded to six decimal places, sufficient for most engineering and academic work
• Large numbers — cubing large inputs may produce results displayed in scientific notation

Tips

1. Use the square root to check geometry problems — a right triangle with legs 3 and 4 has hypotenuse sqrt(25) = 5
2. Switch to cube root when working with volume calculations, such as finding the side length of a cube
3. The reciprocal (1/x) is displayed alongside results, useful for fractions and rate calculations
4. Try custom roots for advanced math problems involving higher-degree equations