$a)\sqrt{{73}^2}=73$

$b)\sqrt{{19}^2\cdot 3^2}=\sqrt{{\left(19\cdot 3\right)}^2}=\sqrt{{57}^2}=57$  

$c)\sqrt{2\cdot 2\cdot 2\cdot 2\cdot 11\cdot 11}=\sqrt{4\cdot 4\cdot 11\cdot 11}=\sqrt{4^2\cdot {11}^2}=\sqrt{{\left(4\cdot 11\right)}^2}=\sqrt{{44}^2}=44$  

$d)\sqrt{{\left(-113\right)}^2}=\sqrt{{113}^2}=113$  

$e)\sqrt{5625}=\sqrt{3\cdot 3\cdot 5\cdot 5\cdot 5\cdot 5}=\sqrt{3\cdot 3\cdot 25\cdot 25}=\sqrt{3^2\cdot {25}^2}=\sqrt{{\left(3\cdot 25\right)}^2}=\sqrt{{75}^2}=75$   

$f)\sqrt{2\sqrt{4}}=\sqrt{2\cdot 2}=\sqrt{2^2}=2$