\(\sqrt{300} + \sqrt{12} = \sqrt{100} ⋅ \sqrt{3} + \sqrt{4} ⋅ \sqrt{3} = 10 \sqrt{3} + 2 \sqrt{3} \text{.}\)

\(10 \sqrt{3} + 2 \sqrt{3} = 12 \sqrt{3} \text{.}\)

\(\sqrt{75} = \sqrt{25} ⋅ \sqrt{3} = 5 \sqrt{3} \text{.}\)

\(3 \sqrt{27} = 3 ⋅ \sqrt{9} ⋅ \sqrt{3} = 3 ⋅ 3 ⋅ \sqrt{3} = 9 \sqrt{3} \text{.}\)

\(4 \sqrt{300} - 2 \sqrt{27} = 4 ⋅ \sqrt{100} ⋅ \sqrt{3} - 2 ⋅ \sqrt{9} ⋅ \sqrt{3} \text{.}\)

\(4 ⋅ 10 ⋅ \sqrt{3} - 2 ⋅ 3 ⋅ \sqrt{3} = 40 \sqrt{3} - 6 \sqrt{3} = 34 \sqrt{3} \text{.}\)

\(\sqrt{\frac{25}{81}} = {\sqrt{25} \over \sqrt{81}} = \frac{5}{9} \text{.}\)