[tex] \bf \sqrt{28}\cdot \sqrt{176}~~
\begin{cases}
28=2\cdot 2\cdot 7\\
\qquad 2^2\cdot 7\\
176=2\cdot 2\cdot 2\cdot 2\cdot 11\\
\qquad 2^2\cdot 2^2\cdot 11\\
\qquad (2^2)^2\cdot 11
\end{cases}\implies \sqrt{2^2\cdot 7}\cdot \sqrt{(2^2)^2\cdot 11}
\\\\\\
2\sqrt{7}\cdot 2^2\sqrt{11}\implies 2\sqrt{7}\cdot 4\sqrt{11}\implies 8\sqrt{7\cdot 11}\implies 8\sqrt{77} [/tex]
