Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ 6\\ b.\ 3\\ c.\ -5\\ d.\ |x+3|-|x+5| \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ \sqrt{\left( 7-\sqrt{3}\right)^{2}} +\sqrt{\left(\sqrt{3} -1\right)^{2}} =7-\sqrt{3} +\sqrt{3} -1=6\\ b.\ \sqrt{23-8\sqrt{7}} +\sqrt{8-2\sqrt{7}} =\sqrt{\left( 4-\sqrt{7}\right)^{2}} +\sqrt{\left( 1-\sqrt{7}\right)^{2}}\\ =4-\sqrt{7} +\sqrt{7} -1=3\\ c.\ \sqrt{\left( 2-\sqrt{5}\right)^{2}} -\sqrt{\left( 7-\sqrt{5}\right)^{2}} =2-\sqrt{5} -7+\sqrt{5} =-5\\ d.\ \sqrt{( x+3)^{2}} -\sqrt{( x+5)^{2}} =|x+3|-|x+5| \end{array}$
