$\sqrt{27} * \sqrt{3} = \sqrt{27 * 3} = \sqrt{81} = 9$

$\sqrt{18} * \sqrt{2} = \sqrt{18 * 2} = \sqrt{36} = 6$

$\sqrt{10} * \sqrt{12,1} = \sqrt{10 * 12,1} = \sqrt{121} = 11$

$\sqrt{0,5} * \sqrt{50} = \sqrt{0,5 * 50} = \sqrt{25} = 5$

$\sqrt{1\frac{3}{7}} * \sqrt{2,8} = \sqrt{1\frac{3}{7} * 2,8} = \sqrt{\frac{10}{7} * \frac{28}{10}} = \sqrt{\frac{1}{1} * \frac{4}{1}} = \sqrt{4} = 2$

$\sqrt{5 * 2^3} * \sqrt{5^3 * 2^3} = \sqrt{5 * 2^3 * 5^3 * 2^3} = \sqrt{5^{1 + 3} * 2^{3 + 3}} = \sqrt{5^{4} * 2^{6}} = \sqrt{5^4} * \sqrt{2^{6}} = \sqrt{(5^2)^2} * \sqrt{(2^3)^2} = |5^2| * |2^3| = |25| * |8| = 25 * 8 = 200$