How do calculators compute square roots?
I was using my calculator and wondered — how does it actually calculate the square root of a number that isn't a perfect square? Like sqrt(2) = 1.41421356... How does it figure that out? Does it just try different numbers until it gets close? Is there a formula? This has been bugging me all week.
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This is actually a much deeper question than it appears on the surface. The simple answer most textbooks give is technically correct but misses a lot of nuance. Let me try to explain it in a way that captures the full picture.
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This is actually a much deeper question than it appears on the surface. The simple answer most textbooks give is technically correct but misses a lot of nuance. Let me try to explain it in a way that captures the full picture.
Don't feel bad for not getting this right away. Some of the smartest people in history spent their whole lives on questions like this. The fact that you're curious enough to ask puts you ahead of most people. Keep asking why.
I'm a physics grad student and this is one of my favorite questions to explain. The key insight is that our everyday intuition doesn't always apply at extreme scales — very small (quantum), very large (cosmological), or very fast (relativistic).
This is something I struggled with until a professor explained it using an analogy that finally clicked. The real world is messy and doesn't always fit neatly into the simplified models we learn in textbooks.
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