\(x\sqrt{y}=-\sqrt{x^2\cdot y}\)

a: \(xy^2\sqrt{x}=\sqrt{x^2y^4\cdot x}=\sqrt{x^3y^4}\)

b: \(\dfrac{2}{x}\sqrt{\dfrac{15xy}{4}}=-\sqrt{\dfrac{4}{x^2}\cdot\dfrac{15xy}{4}}=-\sqrt{\dfrac{15y}{x}}\)

\(=\sqrt{\left(\frac{x}{x-y}\right)^2\cdot\frac{x-y}{x}}\)

\(=\sqrt{\frac{x^2}{\left(x-y\right)^2}\cdot\frac{x-y}{x}}\)

\(=\sqrt{\frac{x}{x-y}}\)

5 y y = ( 5 y ) 2 . y   = 25. y 2 . y = 25. y 3

Chọn đáp án D

a) \(\sqrt{27x^2}=\sqrt{3.\left(3x\right)^2}=\left|3x\right|.\sqrt{3}=3x\sqrt{3}\left(x>0\right)\)

b) \(\sqrt{8xy^2}=\left|y\right|.2\sqrt{2x}=-2y\sqrt{2x}\left(x\ge0,y\le0\right)\)

1) \(x\sqrt{13}=\sqrt{13x^2}\left(x\ge0\right)\)

2) \(x\sqrt{-15x}=-\left|x\right|\sqrt{15x}=-\sqrt{15x^3}\left(x< 0\right)\)

3) \(x\sqrt{2}=-\left|x\right|\sqrt{2}=-\sqrt{2x^2}\left(x\le0\right)\)

a) \(\sqrt{128\left(x-y\right)^2}\)

\(=\sqrt{8^2\cdot2\left(x-y\right)^2}\)

\(=\left|8\left(x-y\right)\right|\sqrt{2}\)

\(=8\left|\left(x-y\right)\right|\sqrt{2}\)

b) \(\sqrt{150\left(4x^2-4x+1\right)}\)

\(=\sqrt{5^2\cdot6\left(2x-1\right)^2}\)

\(=\left|5\left(2x-1\right)\right|\sqrt{6}\)

\(=5\left|2x-1\right|\sqrt{6}\)

c) \(\sqrt{x^3-6x^2+12x-8}\)

\(=\sqrt{\left(x-2\right)^3}\)

\(=\sqrt{\left(x-2\right)^2\left(x-2\right)}\)

\(=\left|x-2\right|\sqrt{x-2}\)

a: \(=\sqrt{64\cdot2\cdot\left(x-y\right)^2}=8\sqrt{2}\cdot\left|x-y\right|\)

b; \(=\sqrt{25\cdot6\left(2x-1\right)^2}=5\sqrt{6}\cdot\left|2x-1\right|\)

c: \(=\sqrt{\left(x-2\right)^3}=\left|x-2\right|\cdot\sqrt{x-2}\)

b)  x - 29 x  với x < 0

= - - 29 x 2 x = - - 29 x