This square-root calculator returns the principal nonnegative root, the corresponding negative solution to x² = n, and a numerical square check.
Math
Square Root Calculator
Calculate the principal square root, corresponding negative root, and square check.
Calculator
About this calculator
Formula notes
For n ≥ 0, the principal root r satisfies r = √n and r² = n. If n > 0, both r and −r solve x² = n.
Worked examples
- Example: √144 = 12, so the two solutions to x² = 144 are 12 and −12, and 12² checks back to 144.
- For 0.0004, the principal square root is 0.02, the corresponding negative root is -0.02, and squaring either returns 0.0004.
How to use it
- Enter a nonnegative radicand.
- Read the principal and corresponding negative roots.
- Use the square check to confirm the displayed result.
Frequently asked questions
Why are there two roots but one square-root value?
The √ symbol denotes the principal nonnegative root; an equation x² = n can additionally have its negative solution.
Can I enter a negative number?
Not in this real-number calculator. Negative radicands require imaginary or complex-number output.
Limits and interpretation
- Real square roots are shown only for nonnegative inputs; negative radicands require complex numbers, which this calculator does not represent.
- Floating-point display and classification can be affected by decimal approximation, especially for very large, very small, or nearly perfect-square values.