Heron's Square Root Method
Approximate the nonnegative square root with Heron's iteration and stop when successive estimates meet a relative tolerance.
Description
Approximate the nonnegative square root with Heron's iteration and stop when successive estimates meet a relative tolerance.
Approximate the nonnegative square root with Heron's iteration and stop when successive estimates meet a relative tolerance.
When to use Heron's Square Root Method
Use this tool to test or transform exact integers according to the named number-theory definition, for education, validation, or algorithm checks.
- value
- A finite numeric input greater than or equal to 0.
- tolerance
- A finite numeric input greater than or equal to 1e-15.
- max Iterations
- An integer input from 1 through 1000.
How the calculation works
Limitations and assumptions
This tool applies an exact integer definition within JavaScript's safe-integer range. It is not an arbitrary-precision factorization or proof system, so do not use rounded measurements or integers beyond the accepted domain as though they were exact.
Alternative or Complementary approaches
Complement a number-property result with its factorization, divisors, digit representation, or a second independent predicate. A true result establishes only the named property and does not imply other properties such as primality.
References
-
Methods of computing square roots — Wikipedia contributors
Similar or alternative tools
- Perfect Square Checker
Check whether a nonnegative safe integer is an exact integer square.
- Perfect Cube Checker
Check whether a safe integer is an exact integer cube.