Answer:
33. yes
34. no
35. yes
36. yes
37. no
38. no
Step-by-step explanation:
The distance between two points on a square grid is the root of the sum of two squares, or it is an integer. That is, the non-integer values must be the root of a 2-element subset of the set of squares: {1, 4, 9, ...}, possibly with repeated values.
The possible sums less than 9 are {2, 5, 8}.
The distances √2, √4=2, and √5 can be drawn on a grid. The others listed in these problems (√3, √6, √7) cannot.
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Additional comment
In general, the length of any square root can be constructed with compass and ruler. That isn't the question here. For this, we're confined to distances between grid points.
