[ELI5]: How do calculators find out the square root of a number?

Question

[ELI5]: How do calculators find out the square root of a number?

In: Mathematics

Answer 1

Depends on the calculator, but here’s one approach, illustrated for square root of 100

1. Make a first estimate (eg half it, your calculator might make a better guess though) = 50.
2. Add that guess to your target divided by that guess, and halve. So (50 + 100/50) / 2 = 26. That’s your next estimate.
3. Continue until the difference between succeeding estimates is small (again depends on your device).

50 -> 26 -> 14.9 -> 10.8 -> 10.03 so it’s getting there very quickly.

Edit: as the other poster said, the actual algorithm used by any given calculator may be a lot more sophisticated.