Question

№1 Упростить выражение a)$11\sqrt{5} +\sqrt{500} -\sqrt{180}$
в)$(\sqrt{6} +\sqrt{3} )^2$
б)$3\sqrt{2}(5\sqrt{2} -\sqrt{32})$
г)$(\sqrt{3} -\sqrt{8} )(\sqrt{8} +\sqrt{3} )$

Answer 1

$\displaystyle 1)11\sqrt{5}+\sqrt{500}-\sqrt{180}=11\sqrt{5}+10\sqrt{5}-6\sqrt{5}=15\sqrt{5}\\\\ 2)(\sqrt{6}+\sqrt{3})^2=6+2\sqrt{18}+3=6+6\sqrt{2}+3=9+6\sqrt{2}\\\\ 3)3\sqrt{2}(5\sqrt{2}-\sqrt{32})=3\sqrt{2}(5\sqrt{2}-2^2\sqrt{2})=3\sqrt{2}(5\sqrt{2}-4\sqrt{2})=3\sqrt{2}\sqrt{2}=3*2=6\\\\ 4)(\sqrt{3}-\sqrt{8})(\sqrt{8}+\sqrt{3})=(\sqrt{3}-2\sqrt{2})(2\sqrt{2}+\sqrt{3})=(\sqrt{3}-2\sqrt{2})(\sqrt{3}+2\sqrt{2})=\\ \\ 3-4*2=3-8=-5$