Question

|1-√51|+|2-√51|+...+|7-√51|+7|8-√51|

Answer 1

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