Đáp án:
$2008-\dfrac{2007}{2008}$
Giải thích các bước giải:
$\sqrt{1+2007^2+\dfrac{2007^2}{2008^2}}$
$=\sqrt{1+2.2007+2007^2-2.2007+\dfrac{2007^2}{2008^2}}$
$=\sqrt{(1+2007)^2-2.2007+\dfrac{2007^2}{2008^2}}$
$=\sqrt{2008^2-2.2008.\dfrac{2007}{2008}+\dfrac{2007^2}{2008^2}}$
$=\sqrt{\bigg{(}2008-\dfrac{2007}{2008}\bigg{)}^2}$
$=\bigg{|}2008-\dfrac{2007}{2008}\bigg{|}$
$=2008-\dfrac{2007}{2008}$.