First, let's simplify [tex]\sqrt{20-\sqrt{19}}[/tex] and [tex]\sqrt{20+\sqrt{19}}[/tex]:

[tex]\sqrt{20-\sqrt{19}} = \sqrt{20}\sqrt{1-\frac{\sqrt{19}}{20}} = \sqrt{20}\sqrt{1}\sqrt{1-\frac{\sqrt{19}}{20}} = \sqrt{20}\sqrt{1-\frac{\sqrt{19}}{20}}[/tex]

[tex]\sqrt{20+\sqrt{19}} = \sqrt{20}\sqrt{1+\frac{\sqrt{19}}{20}} = \sqrt{20}\sqrt{1}\sqrt{1+\frac{\sqrt{19}}{20}} = \sqrt{20}\sqrt{1+\frac{\sqrt{19}}{20}}[/tex]

So, [tex]\sqrt{3} \sqrt{20-\sqrt{19} } \sqrt{20+\sqrt{19} }\sqrt{127} = \sqrt{3}\sqrt{20}\sqrt{1-\frac{\sqrt{19}}{20}}\sqrt{20}\sqrt{1+\frac{\sqrt{19}}{20}}\sqrt{127}[/tex]

[tex]= \sqrt{3}20\sqrt{1-\frac{\sqrt{19}}{20}}\sqrt{1+\frac{\sqrt{19}}{20}}\sqrt{127}[/tex]

[tex]= 20\sqrt{3}\sqrt{1-\frac{19}{20}}\sqrt{1+\frac{19}{20}}*\sqrt{127}[/tex]

[tex]= 20\sqrt{3}\sqrt{\frac{1}{20}}\sqrt{\frac{39}{20}}*\sqrt{127}[/tex]

[tex]= 20\sqrt{3}\frac{1}{\sqrt{20}}\sqrt{39}\sqrt{20}*\sqrt{127}[/tex]

[tex]= 20\sqrt{3}\frac{1}{\sqrt{20}}\sqrt{39}20\sqrt{127}[/tex]

[tex]= 20\sqrt{3}\frac{1}{\sqrt{20}}\sqrt{39}20\sqrt{127}[/tex]

[tex]= 20\sqrt{3}\frac{1}{2\sqrt{5}}\sqrt{39}20\sqrt{127}[/tex]

[tex]= 20\sqrt{3}\frac{\sqrt{39}}{10} \sqrt{127}[/tex]

[tex]= 40\sqrt{3}\sqrt{39}\sqrt{127}[/tex]

[tex]= 40\sqrt{339127}[/tex]

[tex]= \boxed{40\sqrt{14967}}[/tex]