Đáp án:
$a)2\sqrt{2}\\ b)-6\sqrt{3}\\ c)8\sqrt{5}+3\sqrt{3}\\ d)5xy\sqrt{x}$
Giải thích các bước giải:
$a)\sqrt{18}-2\sqrt{32}+3\sqrt{50}-4\sqrt{8}\\ =\sqrt{2.9}-2\sqrt{2.16}+3\sqrt{2.25}-4\sqrt{2.4}\\ =3\sqrt{2}-2.4\sqrt{2}+3.5\sqrt{2}-4.2\sqrt{2}\\ =3\sqrt{2}-8\sqrt{2}+15\sqrt{2}-8\sqrt{2}\\ =3\sqrt{2}-8\sqrt{2}+15\sqrt{2}-8\sqrt{2}\\ =2\sqrt{2}\\ b)3\sqrt{27}+\sqrt{75}-3\sqrt{48}-4\sqrt{12}\\ =3\sqrt{3.9}+\sqrt{3.25}-3\sqrt{3.16}-4\sqrt{3.4}\\ =3.3\sqrt{3}+5\sqrt{3}-3.4\sqrt{3}-4.2\sqrt{3}\\ =9\sqrt{3}+5\sqrt{3}-12\sqrt{3}-8\sqrt{3}\\ =-6\sqrt{3}\\ c)2\sqrt{5}-2\sqrt{108}+3\sqrt{20}+5\sqrt{27}\\ =2\sqrt{5}-2\sqrt{12.9}+3\sqrt{4.5}+5\sqrt{3.9}\ =2\sqrt{5}-2.3\sqrt{12}+3.2\sqrt{5}+5.3\sqrt{3}\\ =2\sqrt{5}-6\sqrt{3.4}+6\sqrt{5}+15\sqrt{3}\\ =2\sqrt{5}-12\sqrt{3}+6\sqrt{5}+15\sqrt{3}\\ =8\sqrt{5}+3\sqrt{3}\\ d)8\sqrt{x^3y^2}-3y\sqrt{x^3}(x \ge 0; y \ge 0)\\ =8\sqrt{x.x^2y^2}-3y\sqrt{x.x^2}\\ =8xy\sqrt{x}-3xy\sqrt{x}\\ =5xy\sqrt{x}$
