$\sqrt{7}(\sqrt{7}-\sqrt{28})=\sqrt{7}(\sqrt{7}-\sqrt{4\ast 7})=\sqrt{7}(\sqrt{7}-2\sqrt{7})=\sqrt{7}\ast (-\sqrt{7})=-7$

$(\sqrt{18}+\sqrt{72})\ast \sqrt{2}=(\sqrt{9\ast 2}+\sqrt{36\ast 2})\ast \sqrt{2}=(3\sqrt{2}+6\sqrt{2})\ast \sqrt{2}=9\sqrt{2}\ast \sqrt{2}=9\ast 2=18$

$(4\sqrt{3}-\sqrt{75}+4)\ast 3\sqrt{3}=(4\sqrt{3}-\sqrt{25\ast 3}+4)\ast 3\sqrt{3}=(4\sqrt{3}-5\sqrt{3}+4)\ast 3\sqrt{3}=(4-\sqrt{3})\ast 3\sqrt{3}=4\ast 3\sqrt{3}-\sqrt{3}\ast 3\sqrt{3}=12\sqrt{3}-3\ast 3=12\sqrt{3}-9$

$(\sqrt{600}+\sqrt{6}-\sqrt{24})\ast \sqrt{6}=(\sqrt{100\ast 6}+\sqrt{6}-\sqrt{4\ast 6})\ast \sqrt{6}=(10\sqrt{6}+\sqrt{6}-2\sqrt{6})\ast \sqrt{6}=9\sqrt{6}\ast \sqrt{6}=9\ast 6=54$