sos!!!!!¡!!! a)~\sqrt{8+2\sqrt{15}}-\sqrt{6+2\sqrt{5}}   b)\sqrt{17-2\sqrt{72}+\sqrt{19+2\sqrt{18}}},c)~\sqrt{12-2\sqrt{32}}+\sqrt{9+4\sqrt{2}}   d)~\sqrt{29-2\sqrt{180}}-\sqrt{9+4\sqrt{5}},e)~~\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{2}   f)\sqrt{6+\sqrt{11}}-\sqrt{6-\sqrt{11}}+3\sqrt{2},g)~\sqrt{8-2\sqrt{15}}-\sqrt{7-2\sqrt{10}}   h)~\sqrt{10-2\sqrt{21}}-\sqrt{9-2\sqrt{14}},i)~~~\sqrt{8-3\sqrt{7}}+\sqrt{4-\sqrt{7}}   i)~~~\sqrt{5+\sqrt{21}}-\sqrt{5-\sqrt{21}},k)~~\sqrt{9-3\sqrt{5}}-\sqrt{9+3\sqrt{5}}   l)\quad(\sqrt{10}-\sqrt{2})\sqrt{4+\sqrt{6-2\sqrt{5}}}

Question

sos!!!!!¡!!! a)~\sqrt{8+2\sqrt{15}}-\sqrt{6+2\sqrt{5}} &nbsp; b)\sqrt{17-2\sqrt{72}+\sqrt{19+2\sqrt{18}}},c)~\sqrt{12-2\sqrt{32}}+\sqrt{9+4\sqrt{2}} &nbsp; d)~\sqrt{29-2\sqrt{180}}-\sqrt{9+4\sqrt{5}},e)~~\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{2} &nbsp; f)\sqrt{6+\sqrt{11}}-\sqrt{6-\sqrt{11}}+3\sqrt{2},g)~\sqrt{8-2\sqrt{15}}-\sqrt{7-2\sqrt{10}} &nbsp; h)~\sqrt{10-2\sqrt{21}}-\sqrt{9-2\sqrt{14}},i)~~~\sqrt{8-3\sqrt{7}}+\sqrt{4-\sqrt{7}} &nbsp; i)~~~\sqrt{5+\sqrt{21}}-\sqrt{5-\sqrt{21}},k)~~\sqrt{9-3\sqrt{5}}-\sqrt{9+3\sqrt{5}} &nbsp; l)\quad(\sqrt{10}-\sqrt{2})\sqrt{4+\sqrt{6-2\sqrt{5}}}

Accepted Answer

a. $\displaystyle \sqrt{8+2\sqrt{15}} -\sqrt{6+2\sqrt{5} \ \ } =\sqrt{\left(\sqrt{3} +\sqrt{5}\right)^{2} \ } -\sqrt{\left(\sqrt{5} +\sqrt{1}\right)^{2}} =\sqrt{3} +\sqrt{5} -\sqrt{5} -\sqrt{1} =-1+\sqrt{3}$
b. GTBT = $\displaystyle \sqrt{\left(\sqrt{9} +\sqrt{8}\right)^{2} +}\sqrt{\left(\sqrt{18} +1\right)^{2}} =\sqrt{9} +\sqrt{8} +\sqrt{18} +1=3+2\sqrt{2} +3\sqrt{2} +1=4+5\sqrt{2}$

c. GTBT = $\displaystyle \sqrt{\left(\sqrt{4} -\sqrt{8}\right)^{2}} +\sqrt{\left( 2\sqrt{2} +1\right)^{2}} =\sqrt{8} -\sqrt{4} +2\sqrt{2} +1=2\sqrt{2} -2+2\sqrt{2} +1=-1+4\sqrt{2}$

d. GTBT = $\displaystyle \sqrt{\left(\sqrt{20} -\sqrt{9}\right)^{2}} -\sqrt{\left(\sqrt{5} +2\right)^{2}} =\sqrt{20} -\sqrt{9} -\sqrt{5} -2=2\sqrt{5} -3-\sqrt{5} -2=-5+\sqrt{5}$