\(\displaystyle \sqrt{{{{a}^{2}}}}\times \sqrt{{{{b}^{2}}+1}}\)
\(\displaystyle \begin{array}{l}=\left| a \right|\times \sqrt{{{{b}^{2}}+1}}\\=2\times \sqrt{{{{{\left( {-\sqrt{3}} \right)}}^{2}}+1}}\\=2\times \sqrt{4}\\=4\end{array}\)
\(\displaystyle \sqrt{{16}}\times \sqrt{{25}}\)
\(\displaystyle \begin{array}{l}=4\times 5\\=20\end{array}\)
\(\displaystyle \sqrt{{{{3}^{2}}\times {{4}^{3}}\times 5}}\)
\(\displaystyle \begin{array}{l}=\sqrt{{{{3}^{2}}}}\times \sqrt{{{{4}^{3}}}}\times \sqrt{5}\\=24\sqrt{5}\end{array}\)
\(\displaystyle \sqrt{{30}}\times \sqrt{{2\frac{2}{3}}}\times \sqrt{{0.4}}\)
\(\displaystyle \begin{array}{l}=\sqrt{{30}}\times \sqrt{{\frac{8}{3}}}\times \sqrt{{\frac{2}{5}}}\\=\sqrt{{30\times \frac{8}{3}\times \frac{2}{5}}}\\=\sqrt{{32}}\\=4\sqrt{2}\end{array}\)
\(\displaystyle \sqrt{{3{{a}^{2}}b}}\times 0.5\times \sqrt{{54b{{c}^{3}}}}\)
\(\displaystyle \begin{array}{l}=a\sqrt{{3b}}\times \frac{1}{2}\times 3c\sqrt{{6bc}}\\=\frac{3}{2}ac\sqrt{{18{{b}^{2}}c}}\\=\frac{9}{2}abc\sqrt{{2c}}\end{array}\)
