[tex]\sqrt{1+3+5+7.....+101}= \\ \\ 1+3+5+................. +101=[/tex]
3=2+1
5=4+1
7=6+1
.....
101=100+1
1+3+..........+101=1+2+1+4+1+6+1+......+100+1=51×1+2(1+2+.............+50)
=51+2×[(50×51)/2]=51+50×51=51(1+50)=51²
[tex]1+2+3+................. +101=51^{2}[/tex]
[tex] \sqrt{1+3+5+.......+101}= \sqrt{51^{2} }=51 [/tex]
