What is a square root?
The square root of a non-negative number x is the non-negative number y such that y times y equals x. We write y = sqrt(x). For example, sqrt(16) = 4 because 4 * 4 = 16. Square roots appear in geometry (Pythagorean theorem), statistics (standard deviation), and algebra.
How to calculate a square root by hand?
For perfect squares, factor into primes and pair identical factors: each pair under the radical becomes one factor outside. Example: 36 = 2^2 * 3^2, so sqrt(36) = 2 * 3 = 6. For other numbers, use long-division style methods or Babylonian / Newton iteration: guess y, then replace y with (y + x/y) / 2 until it stabilizes. This tool uses optimized built-in math and summarizes the logic in the collapsible explanation.
Examples
- sqrt(16) = 4 (perfect square)
- sqrt(2) ~ 1.4142... (irrational; choose decimal places above)
- 5^2 = 25
- Cube root of 27 = 3; cube root of -8 = -2
FAQs
- Is sqrt the same as raising to the 1/2 power?
- For non-negative x, yes: x^(1/2) means the same principal square root in real numbers.
- Why no square root of negative numbers?
- Real square roots of negatives are undefined; complex numbers use i. Use cube root mode for signed roots of odd degree.
- How accurate is the calculator?
- Results use double-precision floating point; you control how many digits are shown (2 to 10).