Square Root Calculator
Calculate square roots and nth roots of numbers with precision and step-by-step solutions. Perfect for geometry, engineering, and mathematical applications with detailed root factorization.
Complete Guide: Square Root Calculator
Everything you need to know about using this tool effectively
This calculator finds square roots, cube roots, and custom nth roots of any non-negative number. It handles whole numbers, decimals, and very large values with high precision. Students and professionals use it for algebra, geometry, and scientific calculations.
A web-based root calculator that computes square roots, cube roots, and arbitrary nth roots with a single input. You type the number and select the root degree, then the tool returns the principal root rounded to your preferred precision. It also indicates whether the result is a perfect root or an irrational approximation.
Algebra homework
Students verify square root and cube root answers from textbook problems without manual computation.
Geometry calculations
Find side lengths from area values or compute diagonal distances using the Pythagorean theorem.
Engineering formulas
Engineers calculate roots when working with formulas involving square roots of stress, frequency, or impedance values.
Financial math
Compute geometric means and compound growth rates that require root extraction.
Scientific notation
Find roots of numbers expressed in scientific notation for physics and chemistry calculations.
Enter the number
Type the number you want to find the root of into the main input field.
Select the root degree
Choose square root, cube root, or enter a custom degree for nth root calculations.
View the result
The calculator displays the principal root value instantly below the input fields.
Adjust precision
Use the decimal places selector to round the result to your desired level of precision.
Copy the result
Select and copy the output value for use in your homework, report, or spreadsheet.
Negative numbers have real cube roots but no real square roots, so the calculator handles these cases differently.
For nth roots of negative numbers, the result is only real when n is an odd integer.
Use higher precision settings when the result feeds into further calculations to reduce rounding error.
Remember that the square root of a product equals the product of the square roots only for non-negative values.
Can I find the square root of a negative number?
Real square roots of negative numbers do not exist because any real number squared gives a positive result. The calculator will indicate when the input is out of range for real roots, though cube roots of negative numbers are supported.
What is an nth root?
The nth root of a number is the value that, when multiplied by itself n times, equals the original number. For example, the cube root (n=3) of 27 is 3 because 3 times 3 times 3 equals 27.
How precise are the results?
The calculator uses double-precision floating-point arithmetic giving about 15 significant digits. You can control how many decimal places are shown in the output.
Does it show whether the root is exact?
Yes, when the input is a perfect square, perfect cube, or perfect nth power, the calculator identifies this and shows the exact integer result.
Can I use this for decimal numbers?
Yes, you can enter decimal values and the calculator will return the root as a decimal. This is useful for approximations in applied math and science.
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