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a) \(\sqrt{36}.\sqrt{121}+\sqrt[3]{-64}-\sqrt[3]{125}\)
\(=6.11+\left(-4\right)-5=66-9=57\)
b) \(\sqrt{75}+\sqrt{\left(\sqrt{3}-2\right)^2}-30\sqrt{\frac{3}{25}}\)
\(=\sqrt{25.3}+\left|\sqrt{3}-2\right|-30.\frac{\sqrt{3}}{\sqrt{25}}\)
\(=5\sqrt{3}+2-\sqrt{3}-30.\frac{\sqrt{3}}{5}\)
\(=5\sqrt{3}+2-\sqrt{3}-6\sqrt{3}=2-2\sqrt{3}\)
c) \(\sqrt{11-4\sqrt{7}}-\frac{12}{1+\sqrt{7}}=\sqrt{7-4\sqrt{7}+4}-\frac{12}{1+\sqrt{7}}\)
\(=\sqrt{\left(\sqrt{7}-2\right)^2}-\frac{12}{1+\sqrt{7}}=\left|\sqrt{7}-2\right|-\frac{12}{1+\sqrt{7}}\)
\(=\left(\sqrt{7}-2\right)-\frac{12}{\sqrt{7}+1}=\frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}+1\right)}{\sqrt{7}+1}-\frac{12}{\sqrt{7}+1}\)
\(=\frac{5-\sqrt{7}}{\sqrt{7}+1}-\frac{12}{\sqrt{7}+1}=\frac{-7-\sqrt{7}}{\sqrt{7}+1}\)
\(=\frac{-\sqrt{7}\left(\sqrt{7}+1\right)}{\sqrt{7}+1}=-\sqrt{7}\)
\(A=2\sqrt{2}+3\sqrt{2}-4\sqrt{2}=\sqrt{2}\)
B=6+18-8=16
\(A=2\sqrt{2}+3\sqrt{2}-4\sqrt{2}=\sqrt{2}\\ B=2\cdot3+3\cdot6-8=6+18-8=16\)
\(M=\dfrac{x^3\left(x^2+x\sqrt[3]{6}+\sqrt[3]{36}\right)}{\left|x^3-3\right|-3}=\dfrac{48\left(4\sqrt[3]{36}+2\sqrt[3]{36}+\sqrt[3]{36}\right)}{48-3-3}\\ M=\dfrac{48\cdot7\sqrt[3]{36}}{42}=8\sqrt[3]{36}\)
\(3\sqrt{144}-5\sqrt{49}+\dfrac{1}{2}\sqrt{36}\)
\(=3.12-5.7+\dfrac{1}{2}.6\)
\(=36-35+3=4\)
\(=\sqrt{25-\sqrt{21}}\left(\sqrt{14}+\sqrt{6}\right)\)