\[\boxed{\text{444\ (444).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \sqrt{6 + 2\sqrt{5}} = \sqrt{5 + 1 + 2\sqrt{5}} =\]
\[= \sqrt{\left( \sqrt{5} \right)^{2} + 2\sqrt{5} + 1^{2}} =\]
\[= \sqrt{\left( \sqrt{5} + 1 \right)^{2}} =\]
\[= \left| \sqrt{5} + 1 \right| = \sqrt{5} + 1\ \]
\[\left( так\ как\ \sqrt{5} + 1 > 0 \right).\]
\[\textbf{б)}\ \sqrt{11 - 4\sqrt{7}} = \sqrt{4 + 7 - 4\sqrt{7}} =\]
\[= \sqrt{\left( \sqrt{7} \right)^{2} - 4\sqrt{7} + 2^{2}} =\]
\[= \sqrt{\left( \sqrt{7} - 2 \right)^{2}} = \left| \sqrt{7} - 2 \right| =\]
\[= \sqrt{7} - 2\ \left( так\ как\ \sqrt{7} > 2 = \sqrt{4} \right)\text{.\ }\]