Question

|1-√51|+|2-√51|+...+|7-√51|+7|8-√51|

Answer 1

$|1- sqrt{51} |+|2- sqrt{51}|+...+|7- sqrt{51} |+7|8- sqrt{51} |= \ =( sqrt{51}-1)+( sqrt{51}-2)+...+ (sqrt{51} -7)+7(8- sqrt{51} )= \ = sqrt{51}-1+ sqrt{51}-2+...+ sqrt{51} -7+56- 7sqrt{51} = \ =7 sqrt{51}-28+56- 7sqrt{51} =56-28=28$