I'm not sure about the depth of this question. For starters, a reasonable approximation of sqrt(2) given those two inequalities would be the average of the bounds. In other words, try calculating the average of 62/45 and 64/45, and see how well this value serves as an approximation of the square root of 2.
I'm asking this because I don't understand how to go about answering a question like this one. Never done it before...
Would it be wise to then write something like this
62/45 = 1.377777777....
64/45 = 1.422222222....
and 63/45 = 1.4
so square root of 2 is approximately 1.4