The square root of 1326
So, there I was, happily working out that the square root of 5,100 is very close to
OK, OK, OK, big aside here. Why is that? I’ll tell you why that is. It’s due to the binomial expansion, in a slightly surprising way:
- So
- Or
.
Lovely stuff. But then in stepped in @shalock, who noted that it’s not even the best such approximation. That would be
Now that – that just seems wrong. We can do something sort of similar, based around 1275.125 – the square of
- So
- Which is, again, approximately
.
I haven’t worked through the higher-order terms, on the grounds that they’re awful. The
As for why