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\(\left(a-b\right)\cdot\sqrt{3}=\sqrt{3\left(a-b\right)^2}\)
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) \(2\sqrt{5a^2}=2\sqrt{5}\left|a\right|=-2a\sqrt{5}\)
b)\(2\sqrt{18a^2}=2.3\sqrt{2}.\left|a\right|=6a\sqrt{2}\)
c)\(\sqrt{-9b^3}=\sqrt{9.\left(-b\right)^3}=3\sqrt{-b}.\left|b\right|=-3b\sqrt{-b}\)
d)\(\sqrt{24a^4b^8}=\sqrt{6.\left(4a^2b^4\right)^2}=2a^2b^4\sqrt{6}\)
a: \(\sqrt{48a^4b^2}=\sqrt{16a^4b^2\cdot3}=4\sqrt{3}\cdot a^2\cdot\left|b\right|\)
\(=-4\sqrt{3}\cdot a^2b\)
b: \(\sqrt{-25x^3}=\sqrt{-25x^2\cdot x}=\left|25x^2\right|\cdot\sqrt{-x}\)
\(=-5x\sqrt{-x}\)
a: \(\sqrt{5a^2}=\left|a\sqrt{5}\right|=-a\sqrt{5}\left(a< =0\right)\)
c: A=\(\sqrt{72a^2b^4}=\sqrt{36a^2b^4\cdot2}=6\sqrt{2}\cdot b^2\cdot\left|a\right|\)
mà a<0
nên \(A=-6\sqrt{2}\cdot ab^2\)
d: \(\sqrt{24a^4b^8}=\sqrt{4a^4b^8\cdot6}=2a^2b^4\cdot\sqrt{6}\)
a: \(13\sqrt{11}=\sqrt{13^2\cdot11}=\sqrt{1859}\)
b: \(-8\sqrt{2}=-\sqrt{64\cdot2}=-\sqrt{128}\)
c: \(a\sqrt{5a}=\sqrt{a^2\cdot5a}=\sqrt{5a^3}\)
d: \(b\sqrt{\dfrac{5}{ab}}=-\sqrt{b^2\cdot\dfrac{5}{ab}}=-\sqrt{\dfrac{5b}{a}}\)
a: \(1.5\sqrt{5}=\sqrt{1.5^2\cdot5}=\sqrt{\dfrac{45}{4}}\)
b: \(-ab^2\cdot\sqrt{5a}=-\sqrt{a^2b^4\cdot5a}=-\sqrt{5a^3b^4}\)
d: \(\dfrac{1}{3}y\sqrt{\dfrac{27}{y^2}}=-\sqrt{\dfrac{1}{9}y^2\cdot\dfrac{27}{y^2}}=-\sqrt{3}\)
c: \(\dfrac{1}{y}\sqrt{19y}=-\sqrt{\dfrac{1}{y^2}\cdot19y}=-\sqrt{\dfrac{19}{y}}\)
a: \(3\sqrt{200}=3\cdot10\sqrt{2}=30\sqrt{2}\)
b: \(-5\sqrt{50a^2b^2}=-5\cdot5\sqrt{2a^2b^2}\)
\(=-25\cdot\left|ab\right|\cdot\sqrt{5}\)
c: \(-\sqrt{75a^2b^3}\)
\(=-\sqrt{25a^2b^2\cdot3b}=-5\left|ab\right|\cdot\sqrt{3b}\)
\(\left(a-b\right)\cdot\sqrt{3}=\sqrt{\left(a-b\right)^2\cdot3}\)
\(-\left(a-b\right)\cdot\sqrt{\dfrac{2}{a-b}}=-\sqrt{\left(a-b\right)^2\cdot\dfrac{2}{a-b}}=-\sqrt{2a-2b}\)