\(\frac{2xy^2}{3ab}\sqrt{\frac{9a^3b^4}{8xy^3}}=\frac{2xy^2}{3ab}\frac{3\sqrt{a^2.a}\sqrt{\left(b^2\right)^2}}{2\sqrt{2xy^2.y}}\)

\(=\frac{2xy^2}{3ab}\frac{3a\sqrt{a}b^2}{2y\sqrt{2xy}}=\frac{6xy^2ab^2\sqrt{a}}{6aby\sqrt{2xy}}=\frac{bxy\sqrt{a}}{\sqrt{2xy}}\)

\(=\frac{bxy\sqrt{2axy}}{2xy}=\frac{b\sqrt{2axy}}{2}\)

\(\sqrt{48\cdot45}=12\sqrt{15}\\ \sqrt{225\cdot17}=15\sqrt{17}\\ \sqrt{a^3b^7}=\left|ab^3\right|\sqrt{ab}=ab^3\sqrt{ab}\\ \sqrt{x^5\left(x-3\right)^2}=\left|x^2\left(x-3\right)\right|\sqrt{x}=x^2\left(x-3\right)\sqrt{x}\)

\(\sqrt{48\cdot45}=4\sqrt{3}\cdot3\sqrt{5}=12\sqrt{15}\)

\(\sqrt{225\cdot17}=15\sqrt{17}\)

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

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

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

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

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

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

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

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