Evaluate \(\lceil\sqrt{5}\rceil + \lceil\sqrt{6}\rceil + \lceil\sqrt{7}\rceil + \cdots + \lceil\sqrt{29}\rceil\). Note: For a real number x,\(\lceil x \rceil\) 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 \(\lceil\sqrt{5}\rceil + \lceil\sqrt{6}\rceil + \lceil\sqrt{7}\rceil + \cdots + \lceil\sqrt{29}\rceil=\boxed{106}\)
