\(\sqrt{8} + \sqrt{50} = \sqrt{4} ⋅ \sqrt{2} + \sqrt{25} ⋅ \sqrt{2} = 2 \sqrt{2} + 5 \sqrt{2} \text{.}\)

\(2 \sqrt{2} + 5 \sqrt{2} = 7 \sqrt{2} \text{.}\)

\(\sqrt{18} = \sqrt{9} ⋅ \sqrt{2} = 3 \sqrt{2} \text{.}\)

\(6 \sqrt{700} = 6 ⋅ \sqrt{100} ⋅ \sqrt{7} = 6 ⋅ 10 ⋅ \sqrt{7} = 60 \sqrt{7} \text{.}\)

\(2 \sqrt{500} - 5 \sqrt{20} = 2 ⋅ \sqrt{100} ⋅ \sqrt{5} - 5 ⋅ \sqrt{4} ⋅ \sqrt{5} \text{.}\)

\(2 ⋅ 10 ⋅ \sqrt{5} - 5 ⋅ 2 ⋅ \sqrt{5} = 20 \sqrt{5} - 10 \sqrt{5} = 10 \sqrt{5} \text{.}\)

\(\sqrt{1\frac{13}{36}} = \sqrt{\frac{49}{36}} = {\sqrt{49} \over \sqrt{36}} = \frac{7}{6} = 1\frac{1}{6} \text{.}\)