1) \(\sqrt{30.120}-\sqrt{2,5.14,4}\)
\(=\sqrt{3600}-\sqrt{36}\)
\(=60-6\)
\(=54\)
2) \(\sqrt{5}.\sqrt{80}+\dfrac{\sqrt{16,9}}{\sqrt{0,1}}\)
\(=\sqrt{5.80}+\sqrt{\dfrac{16,9}{0,1}}\)
\(=\sqrt{400}+\sqrt{169}\)
\(=20+13\)
\(=33\)
3) \(\sqrt{\left(2-\sqrt{5}\right)^2}-\dfrac{\sqrt{15}+\sqrt{55}}{\sqrt{3}+\sqrt{11}}\)
\(=\left|2-\sqrt{5}\right|-\dfrac{\sqrt{5}.\left(\sqrt{3}+\sqrt{11}\right)}{\sqrt{3}+\sqrt{11}}\)
\(=\sqrt{5}-2-\sqrt{5}\)
\(=-2\)
4) \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}-\sqrt{2}\right)+\left(2+\sqrt{3}\right)\)
\(=\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)^2}.\sqrt{2}.\left(\sqrt{3}-1\right)\)
\(=\sqrt{\left(2-\sqrt{3}\right)\left(\sqrt{2}+\sqrt{3}\right)\left(2+\sqrt{3}\right)}.\sqrt{2}\left(\sqrt{3}-1\right)\)
\(=\sqrt{\left(2+\sqrt{3}\right)}.\sqrt{2}\left(\sqrt{3}-1\right)\)
\(=\sqrt{\left(2+\sqrt{3}\right).\left(\sqrt{3}-1\right)^2}.\sqrt{2}\)
\(=\sqrt{\left(2+\sqrt{3}\right)\left(3-2\sqrt{3}+1\right)}.\sqrt{2}\)
\(=\sqrt{6-4\sqrt{3}+2+3\sqrt{3}-6+\sqrt{3}}.\sqrt{2}\)
\(=\sqrt{2}.\sqrt{2}\)
\(=2\)
