\(a.\sqrt{100}-\sqrt{25}+\sqrt{16}=\sqrt{10^2}-\sqrt{5^2}+\sqrt{4^2}=10-5+4=9\)
\(b.\sqrt{\dfrac{1}{4}}+\sqrt{\dfrac{25}{9}}-\sqrt{\dfrac{9}{100}}=\dfrac{\sqrt{1}}{\sqrt{4}}+\dfrac{\sqrt{25}}{\sqrt{9}}-\dfrac{\sqrt{9}}{\sqrt{100}}=\dfrac{1}{2}+\dfrac{5}{3}-\dfrac{3}{10}=\dfrac{28}{15}\)
\(c.\dfrac{1}{5}\left(5\sqrt{18}-3\sqrt{27}+2\sqrt{12}\right):\sqrt{3}=\dfrac{1}{5}\left(5\sqrt{3^2.2}-3\sqrt{3^2.3}+2\sqrt{3.2^2}\right):\sqrt{3}=\dfrac{1}{5}\left(15\sqrt{2}-9\sqrt{3}+4\sqrt{3}\right):\sqrt{3}=\dfrac{1}{5}\left(15\sqrt{2}-5\sqrt{3}\right):\sqrt{3}=\left(3\sqrt{2}-\sqrt{3}\right):\sqrt{3}=\sqrt{6}-1\)
\(d.\sqrt{\left(\sqrt{3}-\sqrt{1}\right)^2}+\sqrt{\left(\sqrt{4}-\sqrt{3}\right)^2}=\left|\sqrt{3}-\sqrt{1}\right|+\left|\sqrt{4}-\sqrt{3}\right|=\sqrt{3}-1+2-\sqrt{3}=1\)
