Question

sqrt2 is not a rational number. Therefore, there are rational numbers whose squares are very close to two. For instance, if you square the rational number 140/99 you obtain 1.9998. Try finding other rational numbers that are even closer to 2 and explain how you did it. Help anyone?

Answer 1

A cheap but effective way is to add a little more to 1.9998. On my calculator, (140/99)^2 is closer to 1.9997959, if you add 0.0002, then you'll get 1.99999959.

Answer 2

Maybe try (140/99)+(72/1000000)

Answer 3

Another way is to get an approximation to sqrt(2) and truncate it somewhere, say at 1.4142 and express that number as a fraction: 14142/10000.
That reduces to 7071/5000, and if you square it gives 1.99996..