Question

[Phạm NI NA]

Thực hiện phép tính:

a/ \(\sqrt{3}-2\sqrt{48}+3\sqrt{75}-4\sqrt{108}\)

b/ \(\left(a.\sqrt{\dfrac{a}{b}}+2\sqrt{ab}+b\sqrt{\dfrac{b}{a}}\right)\sqrt{\dfrac{a}{b}}\)

c/ \(^3\sqrt{27}-^3\sqrt{-8}-^3\sqrt{125}\)

d/ \(3+\sqrt{18}+\sqrt{3}+\sqrt{8}\)

e/ \(^3\sqrt{\dfrac{135}{^{3\sqrt{5}}}}-^3\sqrt{54}.^3\sqrt{4}\)

f/ \(^3\sqrt{8a^3-5a}\)

Answer 1

[Mysterious Person]

a) \(\sqrt{3}-2\sqrt{48}+3\sqrt{75}-4\sqrt{108}\)

= \(\sqrt{3}-8\sqrt{3}+15\sqrt{3}-24\sqrt{3}\)

= \(-16\sqrt{3}\)

b) \(\left(a.\sqrt{\dfrac{a}{b}}+2\sqrt{ab}+b.\sqrt{\dfrac{b}{a}}\right)\sqrt{\dfrac{a}{b}}\)

= \(\dfrac{a^2}{b}+2a+b\) = \(\dfrac{a^2+\left(2a+b\right)b}{b}\) = \(\dfrac{a^2+2ab+b^2}{b}\) = \(\dfrac{\left(a+b\right)^2}{b}\)

c) \(\sqrt[3]{27}-\sqrt[3]{-8}-\sqrt[3]{125}\) = \(3+2-5=0\)

d) \(3+\sqrt{18}+\sqrt{3}+\sqrt{8}\) = \(3+3\sqrt{2}+\sqrt{3}+2\sqrt{2}\)

= \(3+\sqrt{3}+5\sqrt{2}\)