Evaluate ⌈√5⌉+⌈√6⌉+⌈√7⌉+⋯+⌈√29⌉. Note: For a real number x,⌈x⌉ denotes the smallest integer that is greater than or equal to x.
+1262 it equals 3+3+3+3+3 for the ones below 9 and 4+4+4+4+4+4+4 for the ones from 10 ~16 and 5+5+5+5+5+5+5+5+5 for the ones 17~25 and 6+6+6 for 26~29 when we add them together we have 3+3+3+3+3+4+4+4+4+4+4+4+5+5+5+5+5+5+5+5+5+6+6+6=106 so our final answer is ⌈√5⌉+⌈√6⌉+⌈√7⌉+⋯+⌈√29⌉=106
