What is a square root calculator?
A square root calculator finds the value that produces the original number when multiplied by itself. For example, √81 = 9 because 9 × 9 = 81. For more power and root operations, use the Exponent Calculator.
How does the square root calculator work?
For a nonnegative number x, the calculator evaluates √x with the browser's square-root function. If Complex mode is selected and x is negative, it calculates √|x| and appends i to represent the principal complex result.
What formula does a square root use?
You can use the Fraction Calculator when a related calculation contains rational values.
How do you use this square root calculator?
- Choose Real numbers or Complex numbers allowed.
- Enter the number whose square root you want.
- Select Calculate Square Root.
- Review the root, perfect-square check, and squared verification.
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Square root examples
√144 = 12, √2 ≈ 1.4142135624, and in Complex mode √−9 = 3i. For everyday comparisons and proportions, the Ratio Calculator and Percentage Calculator are also available.
What are the limits of this calculator?
The calculator accepts finite browser numbers. Real mode rejects negative inputs because they do not have real square roots. Very large or very small results may be displayed in scientific notation, and irrational roots are rounded for readability.
Worked example: Square Root
Enter the following values in the Square Root Calculator and calculate to reproduce this result.
- Number system: Real numbers
- Number: 144
Example result: 12. The principal square root of 144 is 12.
Calculation used: √144 = 12
How to interpret this example
The principal square root is the nonnegative root, so √144 = 12. The equation x² = 144 has two real solutions, +12 and −12. Those are related but different questions.
Frequently asked questions about square roots
Methodology and calculation scope
Calculations use JavaScript double-precision numbers. Perfect-square detection is only reported when the nonnegative input and resulting integer are within the range where the check is reliable.