[tex]\sqrt{200} + \sqrt{500} + \sqrt{8} - \sqrt{45} = \\\\ \sqrt{100 \times 2} + \sqrt{100 \times 5} + \sqrt{4 \times 2} - \sqrt{9 \times 5} = \\\\ \sqrt{10^2 \times 2} + \sqrt{10^2 \times 5} + \sqrt{2^2 \times 2} - \sqrt{3^2 \times 5} = \\\\ 10\sqrt{2} + 10\sqrt{5} + 2\sqrt{2} - 3\sqrt{5} = \\\\ \sqrt{2} \times (10 + 2) + \sqrt{5} \times (10 - 3) = \\\\ \boxed{12\sqrt{2} + 7\sqrt{5}}[/tex]
