$0,2\sqrt{200} = \sqrt{0,2^2 * 200} = \sqrt{\frac{4}{100} * 200} = \sqrt{4 * 2} = \sqrt{8}$
$\sqrt{8} < 10\sqrt{8}$
$0,2\sqrt{200} < 10\sqrt{8}$

$7\sqrt{\frac{32}{49}} = \frac{7\sqrt{32}}{7} = \sqrt{32}$
$0,8\sqrt{50} = \frac{4}{5}\sqrt{50} = \sqrt{\frac{16}{25} * 50} = \sqrt{16 * 2} = \sqrt{32}$

$0,5\sqrt{108} = \frac{1}{2}\sqrt{108} = \sqrt{\frac{108}{4}} = \sqrt{27}$
$9\sqrt{3} = \sqrt{81 * 3} = \sqrt{243}$
$\sqrt{27} < \sqrt{243}$
$0,5\sqrt{108} < 9\sqrt{3}$

$\frac{5}{2}\sqrt{63} = \sqrt{\frac{25}{4} * 63} = \sqrt{\frac{1575}{4}}$
$4,5\sqrt{28} = \frac{9}{2}\sqrt{28} = \sqrt{\frac{81}{4} * 28} = \sqrt{\frac{2268}{4}}$
$\sqrt{\frac{1575}{4}} < \sqrt{\frac{2268}{4}}$
$\frac{5}{2}\sqrt{63} < 4,5\sqrt{28}$