[tex]3\sqrt{32} +\sqrt{72} -2\sqrt{200} =\\3*4\sqrt{2} +6\sqrt{2} -2*10\sqrt{2} =\\12\sqrt{2} +6\sqrt{2} -20\sqrt{2} =-2\sqrt{2}[/tex]
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[tex]2\sqrt{3} (\sqrt{3} -3\sqrt{5} )-4\sqrt{5} (6\sqrt{3} +\sqrt{5} )=\\2\sqrt{9} -6\sqrt{15} -24\sqrt{15} +4\sqrt{25} =\\2*3-30\sqrt{15} +4*5=\\6-30\sqrt{15} +20=\\-14-30\sqrt{15}[/tex]
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[tex](3\sqrt{2} -3\sqrt{5} )(4\sqrt{5} +2\sqrt{2} )=\\3\sqrt{2} *2\sqrt{2} -3\sqrt{5} *4\sqrt{5}+6\sqrt{10} =\\6\sqrt{4} -12\sqrt{25} +6\sqrt{10} =\\6*2-12*5+6\sqrt{10} =\\12-60+6\sqrt{10} =\\-48+6\sqrt{10}[/tex]
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[tex]\sqrt{(8-5\sqrt{3})^2 } -\sqrt{(3\sqrt{3}-5)^2 } =\\|8-5\sqrt{3}| -|3\sqrt{3} -5|=\\8-8\sqrt{3} -5=\\13-8\sqrt{3}[/tex]
