You can approximate irrational square roots with rational numbers using linear interpolation between the integers as follows:

√1 = 1
√2 ≈ 4/3
√3 ≈ 5/3
√4 = 2
√5 ≈ 11/5
√6 ≈ 12/5
√7 ≈ 13/5
√8 ≈ 14/5
√9 = 3
etc...

How good an approximation is this?
For large numbers, might the previous or next fraction be a better approximation?

I like the current comments even though they don't quite get to what I was looking for.

I know these aren't the best approximations, but how big an error is there?  Is there a max or does it increase for large numbers?

Might (with larger numbers but looking at my chart) a number such as 14/5 be a better approximation for √7 than 13/5?

Posted by Jer on 2015-02-18 21:59:23