Let us see.
36 = yes, 62
37 = no
38 = no
39 = no
40 = no
41 = no
42 = no
43 = no
44 = no
45 = no
46 = no
47 = no
48 = no
49 = yes, 72
50 = no
51 = no
52 = no
53 = no
54 = no
55 = no
56 = no
57 = no
58 = no
59 = no
Looks like only two, 36 and 49, are perfect squares.
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683 perfect squares.
They are: 36 49 and 64 which makes three of them
1900
sqrt(2000) = 44.7sqrt(20000) = 141.4So the perfect squares between 2000 and 20000 are the squares of 45 to 141 (inclusive)ie there are 97 perfect squares in the interval.
To find the perfect squares between 35 and 111, we need to determine the perfect squares closest to these numbers. The closest perfect squares are 36 (6^2) and 100 (10^2). The perfect squares between 36 and 100 are 49 (7^2), 64 (8^2), and 81 (9^2). Therefore, there are 4 perfect squares between 35 and 111: 36, 49, 64, and 81.