Sử dụng phép khai phương một tích và khai phương một thương tính giá trị biểu thức.
a, $(\sqrt{12}-3\sqrt{75}).\sqrt{3}$ = $\sqrt{12}.\sqrt{3}-3\sqrt{75}.\sqrt{3}$
= $\sqrt{12.3}-3\sqrt{75.3}$ = $\sqrt{36}-3\sqrt{225}$ = 6 - 3.15 = -39
b, $\sqrt{80}.\sqrt{34}.\sqrt{25}.\sqrt{170}$ = $\sqrt{2.4.10}.\sqrt{2.17}.\sqrt{25}.\sqrt{10.17}$
= $\sqrt{2}.\sqrt{4}.\sqrt{10}.\sqrt{2}.\sqrt{17}.\sqrt{25}.\sqrt{10}.\sqrt{17}$
=$(\sqrt{2}.\sqrt{2}).\sqrt{4}.(\sqrt{10}.\sqrt{10}).(\sqrt{17}.\sqrt{17}).\sqrt{25}$
= 2.2.10.17.5 = 3400
c, $\sqrt{3\frac{1}{16}.2\frac{14}{25}.2\frac{63}{81}}$
= $\sqrt{\frac{49}{16}.\frac{64}{25}.\frac{225}{81}}$
= $\sqrt{\frac{49}{16}}.\sqrt{\frac{64}{25}}.\sqrt{\frac{225}{81}}$
= $\frac{7}{4}.\frac{8}{5}.\frac{15}{9}$ = $\frac{14}{3}$
d, $(\sqrt{20}-3\sqrt{45}+6\sqrt{180}):\sqrt{5}$
= $\sqrt{4.5}:\sqrt{5}-3\sqrt{9.5}:\sqrt{5}+6\sqrt{36.5}:\sqrt{5}$
= $\sqrt{4}.\sqrt{5}:\sqrt{5}-3\sqrt{9}.\sqrt{5}:\sqrt{5}+6\sqrt{36}.\sqrt{5}:\sqrt{5}$
= 2 - 3.3 + 6.6 = 29