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

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

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

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

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

c.\(\sqrt{\frac{x^4}{\left(x-5\right)^2}\cdot\frac{x-5}{3x}}=\sqrt{\frac{x^3}{3\left(x-5\right)}}\)

\(-2\sqrt{-a}=\sqrt{\left(-2\right)^2\cdot-a}=\sqrt{-4a}\)

\(\frac{1}{x-y}.\sqrt{x^4\left(x^2+y^2-2xy\right)}\)

\(=\frac{1}{x-y}.\sqrt{\left(x^2\right)^2.\left(x-y\right)^2}\)

\(=\frac{1}{x-y}\left(x-y\right)x^2\)

\(=x^2\)

chịu.-.

HT~~~

a, -2x^2y căn 7 

b, ab^2 căn 63 

c, a-1 căn 147a-147

d, y+2 nhân căn [192 nhân (y+2)^3]

a)-2x²y√7

b) 3ab²√7

c) 7(a-1)√3(a-1)

d) 8(y+2)²√3(y+2)

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

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

a)\(=-\sqrt{\left(\frac{a}{b}\right)^2\cdot\frac{b}{a}}\)

\(=-\sqrt{\frac{a^2}{b^2}\cdot\frac{b}{a}}\)

\(=-\sqrt{\frac{a}{b}}\)

b) \(=\sqrt{\left(\frac{1}{2x-1}\right)^2\cdot5\left(4x^2-4x+1\right)}\)

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

\(=\sqrt{5}\)

c)\(=\sqrt{\left(x-5\right)^2\cdot\frac{-3}{\left(x-5\right)\left(x+5\right)}}\)

\(=\sqrt{\frac{-3\left(x-5\right)}{x+5}}\)

\(=\sqrt{\frac{15-3x}{x+5}}\)

\(x\sqrt{\dfrac{2}{x}}=\sqrt{x^2\cdot\dfrac{2}{x}}=\sqrt{2x}\)

\(x\sqrt{\dfrac{2}{5}}=\sqrt{\dfrac{2}{5}\cdot x^2}=\sqrt{\dfrac{2x^2}{5}}\)

\(\left(x-5\right)\cdot\sqrt{\dfrac{x}{25-x^2}}=\sqrt{\left(x-5\right)^2\cdot\dfrac{x}{-\left(x-5\right)\left(x+5\right)}}=\sqrt{-\dfrac{x\left(x-5\right)}{x+5}}\)

\(x\sqrt{\dfrac{7}{x^2}}=\sqrt{x^2\cdot\dfrac{7}{x^2}}=\sqrt{7}\)

a) \(\sqrt{25\cdot96}=\sqrt{5^2\cdot2^5\cdot3}=\sqrt{5^2\cdot\left(2^2\right)^2\cdot2\cdot3}\)

\(=20\sqrt{6}\)

b) \(\sqrt{21\cdot75\cdot14}=\sqrt{2\cdot3^2\cdot5^2\cdot7^2}=105\sqrt{2}\)

c) \(y^2\sqrt{x^6\cdot y^8}=\sqrt{x^6\cdot y^4\cdot y^8}=\sqrt{\left(x^3\right)^2\cdot\left(y^6\right)^2}=x^3\cdot y^6\)

hì,giúp bn đc phần a thôi nha!!!

\(a,\sqrt{25.96}=\sqrt{25.16.6}=\sqrt{25}.\sqrt{16}.\sqrt{6}=5.4.\sqrt{6}=20\sqrt{6}\)

=.= hok tốt!!!

d) \(a^3.\sqrt{a^5.\left(a-3\right)^2}=a^3.\sqrt{a^5}.\sqrt{\left(a-3\right)^2}=a^3.\sqrt{a^5}.\left(a-3\right)\)