97 + 99 = 196
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They are: 97+99 = 196
144 + 196 = 340 so integers are 12 & 14.
x^2 + (x+1 )^2 =365 x^2 +x^2 + 2x +1 =365 2x^2 + 2x = 364 x^2 + x = 182 = (x- 13)(x + 14) x =13, so integers are 13 and 14, squares 169 and 196, which total 365.
The numbers are 195, 196, 197 and 198.
169 < 179 < 196 So, sqrt(169) < sqrt(179) < sqrt(196) and so, 13 < sqrt(179) < 14