[tex] \\ \sqrt{9900} =
\\
\\ \sqrt{2^2\cdot \:3^2\cdot \:5^2\cdot \:11} =>
\\
\\ \boxed{\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}}
\\
\\ \sqrt{11}\sqrt{2^2}\sqrt{3^2}\sqrt{5^2} =>
\\
\\ \boxed{\sqrt[n]{a^n}=a}
\\
\\ 2\sqrt{11}\sqrt{3^2}\sqrt{5^2} =>
\\
\\ 2\cdot \:3\sqrt{11}\sqrt{5^2} =>
\\
\\ 2\cdot \:3\cdot \:5\sqrt{11} => \boxed{30\sqrt{11}} [/tex]
[tex] \it \sqrt{9900}=\sqrt{11\cdot9\cdot100} =3\cdot10\sqrt{11} =30\sqrt{11} [/tex]
