a) \(\sqrt{5}.\sqrt{1,2}.\sqrt{24}\)
\(=\sqrt{5.1,2.24}\)
\(=\sqrt{144}\)
\(=12\)
b) \(\dfrac{\sqrt{4444}}{\sqrt{1111}}=\sqrt{\dfrac{4444}{1111}}=\sqrt{4}=2\)
c) \(\sqrt{\dfrac{3}{5}}+\sqrt{\dfrac{5}{3}}-\dfrac{1}{2}\sqrt{60}\)
\(=\dfrac{\sqrt{3.5}}{5}+\dfrac{\sqrt{5.3}}{3}-\dfrac{1}{2}\sqrt{4.15}\)
\(=\dfrac{\sqrt{15}}{5}+\dfrac{\sqrt{15}}{3}-\sqrt{15}\)
\(=\dfrac{3\sqrt{15}+5\sqrt{15}-15\sqrt{15}}{15}\)
\(=\dfrac{-7\sqrt{15}}{15}\)
d) \(\sqrt{5+2\sqrt{6}}+\sqrt{5-2\sqrt{6}}\)
\(=\sqrt{\left(\sqrt{3}\right)^2+2.\sqrt{3}.\sqrt{2}+\left(\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}\right)^2-2.\sqrt{3}.\sqrt{2}+\left(\sqrt{2}\right)^2}\)
\(=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)+\left(\sqrt{3}-\sqrt{2}\right)\)
\(=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}\)
\(=2\sqrt{3}\)
