\[\boxed{\mathbf{1255}\mathbf{.}}\]
\[1)\ \sqrt{a^{4} \bullet \left( 9a^{2} - 6a + 1 \right)} =\]
\[= \sqrt{a^{4} \bullet (3a - 1)^{2}} = a^{2} \bullet |3a - 1|\]
\[2)\ \sqrt{b^{2} \bullet \left( 4b^{4} + 4b^{2} + 1 \right)} =\]
\[= \sqrt{b^{2} \bullet \left( 2b^{2} + 1 \right)^{2}} =\]
\[= |b| \bullet \left( 2b^{2} + 1 \right)\]