Question

cat face radical din 9900?
$\sqrt{9900}$

Answer 1

$\\ \sqrt{9900} = \\ \\ \sqrt{2^2\cdot \:3^2\cdot \:5^2\cdot \:11} => \\ \\ \boxed{\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}} \\ \\ \sqrt{11}\sqrt{2^2}\sqrt{3^2}\sqrt{5^2} => \\ \\ \boxed{\sqrt[n]{a^n}=a} \\ \\ 2\sqrt{11}\sqrt{3^2}\sqrt{5^2} => \\ \\ 2\cdot \:3\sqrt{11}\sqrt{5^2} => \\ \\ 2\cdot \:3\cdot \:5\sqrt{11} => \boxed{30\sqrt{11}}$

Answer 2

$\it \sqrt{9900}=\sqrt{11\cdot9\cdot100} =3\cdot10\sqrt{11} =30\sqrt{11}$