\[\boxed{\text{453\ (453).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \sqrt{a + 2\sqrt{a - 1}} =\]
\[= \sqrt{(a - 1) + 1 + 2\sqrt{a - 1}} =\]
\[= \sqrt{\left( \sqrt{a - 1} + 1 \right)^{2}} = \sqrt{a - 1} + 1\]
\[= \sqrt{a + b} + 1 - \sqrt{a + b} + 1 = 2\]