Question

If each small square on a grand chess board is 2 cm by 2 cm, each diagonal
of the whole board measures 800 cm. How many small squares are on the
board?

Answer 1

?? The sides appear not to be integers. I guess there must be a border included in the length.

√800 = 20√2

So, I guess there are 10√2 small squares across and down.

Answer 2

If they were 1 by 1 the diagonal would be 400

say n of them along each side
diagonal is then n sqrt 2 =400
n = 400/sqrt 2
but n^2 is number of squares
so
answer = 400^2/2 =200*400 = 80,000
I suspect you mean the diagonal is 80 cm, not 800 by the way