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$1) \sqrt{5} \times \sqrt{20} = \sqrt{5 \times 20} = \sqrt{100} = 10$
$2) \sqrt{125} \div \sqrt{5} = \sqrt{125 \div 5} = \sqrt{25} = 5$
$3) {( \sqrt{7} )}^{2} = \sqrt{7} \times \sqrt{7} = \sqrt{7 \times 7} = \sqrt{49} = 7$
$4) \frac{ {10}^{3} }{ \sqrt{10000} } = \frac{1000}{100} = 10$
$5){(5 \sqrt{2})}^{2} = {5}^{2} \times { (\sqrt{2}) }^{2} = 25 \times 2 = 100$
$\sqrt{50} - 2 \sqrt{2} = \sqrt{2 \times 25} - 2 \sqrt{2} = 5 \sqrt{2} - 2 \sqrt{2} = 3 \sqrt{2}$
7)
$\sqrt{3} + \sqrt{3} + \sqrt{3} = 3 \sqrt{3}$
8)
$18 \sqrt{5} \times 2 \sqrt{5} = 18 \times 2 \times 5 = 180$
9)
$\sqrt{ {15}^{2} } = 15$
10)
$\sqrt{72} = \sqrt{8 \times 9} = \sqrt{2 \times 4} \times \sqrt{9} = 2 \times 3 \sqrt{2} = 6 \sqrt{2}$
11)
$\sqrt{ {8}^{4} } \div 16 = {8}^{2} \div 16 = 64 \div 16 = 4$
12)
$\sqrt{ {(5 - \sqrt{50}) }^{2} } = 5 - \sqrt{50}$
13)
$\sqrt{ {16}^{2} - {9}^{2} } = \sqrt{(16 - 9)(16 + 9)} = \\ \sqrt{7 \times 25} = 5 \sqrt{7}$
14)
$\sqrt{ {3}^{2} \times {2}^{4} \times 9 } = 3 \times 4 \times 3 = 36$
15)
$3 \sqrt{2} = \sqrt{2 \times {3}^{2} } = \sqrt{18}$
16)
$\frac{ \sqrt{24} }{ \sqrt{6} } = \sqrt{ \frac{24}{6} } = \sqrt{4} = 2$
17)
$\sqrt{125} \times \sqrt{8} = \sqrt{5 \times 25 \times 4 \times 2} = 10 \sqrt{10}$