a) Ta có: \(-7xy\cdot\sqrt{\dfrac{3}{xy}}\)

\(=\dfrac{-7xy\cdot\sqrt{3xy}}{xy}\)

\(=-7\sqrt{3}\cdot\sqrt{xy}\)

b) Ta có: \(ab+b\sqrt{a}+\sqrt{a}+1\)

\(=b\sqrt{a}\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)\)

\(=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)

$a)-7xy.\sqrt{\dfrac{3}{xy}}$

$=-7.\sqrt{x^2y^2.\dfrac{3}{xy}}(do \,x,y>0a\to xy>0)$

$=-7.\sqrt{\dfrac{xy}{3}}$

$b)ab+b\sqrt{a}+\sqrt{a}+1(a \ge 0)$

$=b\sqrt{a}(\sqrt{a}+1)+\sqrt{a}+1$

$=(\sqrt{a}+1)(b\sqrt{a}+1)$

a) \(-7xy.\sqrt{\dfrac{3}{xy}}=-7xy.\dfrac{\sqrt{3xy}}{xy}=-7\sqrt{3xy}\)

b) \(ab+b\sqrt{a}+\sqrt{a}+1=b\sqrt{a}\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)

a: \(-7xy\cdot\sqrt{\dfrac{3}{xy}}=-7xy\cdot\dfrac{\sqrt{3}}{\sqrt{xy}}=-7\sqrt{3xy}\)

b: \(ab+b\sqrt{a}+\sqrt{a}+1\)

\(=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)

) x y \sqrt{\dfrac{x}{y}}=x y \sqrt{\dfrac{x y}{y^{2}}}=\dfrac{x y}{y} \sqrt{x y}=x \sqrt{x y} .xyyx​​=xyy2xy​​=yxy​xy​=xxy​.

b) \dfrac{x}{y} \sqrt{\dfrac{x}{y}}=\dfrac{x}{y} \sqrt{\dfrac{x y}{y^{2}}}=\dfrac{x}{y^{2}} \sqrt{x y} .yx​yx​​=yx​y2xy​​=y2x​xy​.

c) \sqrt{\dfrac{1}{a}+\dfrac{1}{a^{2}}}=\sqrt{\dfrac{a+1}{a^{2}}}=\dfrac{\sqrt{a+1}}{a} .a1​+a21​​=a2a+1​​=aa+1​​.

d) \sqrt{\dfrac{4 x^{3}}{25 y}}=\sqrt{\dfrac{4 x^{2} x y}{25 y^{2}}}=\dfrac{2 x}{5 y} \sqrt{x y} .25y4x3​​=25y24x2xy​​=5y2x​xy​.

e) 2 a b \sqrt{\dfrac{3}{a b}}=2\sqrt{\dfrac{3(ab)^2}{ab}}=2\sqrt{3ab}2abab3​​=2ab3(ab)2​​=23ab​.

a, GTTĐ x nhân căn xy

b,x/y^2 nhân xăn xy

c,  căn( a+1)/a

d, 2x căn (xy)/5y

e, 2 nhân căn (3ab) 

a) x căn xy

b) x/y^2 căn xy

c) căn a+1/a

d) 2x/5y căn xy

e) 2 căn 3ab

bạn làm rồi nên mk chỉ viết kq thôi nhé :)

a)\(\dfrac{4\sqrt{6x}}{3}\)

b)\(\left(2-y\right)\sqrt{xy}\)

a: \(=6\cdot\sqrt{\dfrac{2xy}{4y^2}}\)

\(=6\cdot\dfrac{\sqrt{2xy}}{-2y}=-\dfrac{3\sqrt{2xy}}{y}\)

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

(do xy > 0 (gt) nên đưa thừa số xy vào trong căn để khử mẫu)

#Học tốt!!!

\(ab\cdot\sqrt{\dfrac{a}{b}}=a\cdot\sqrt{ab}\)

\(\dfrac{a}{b}\cdot\sqrt{\dfrac{b}{a}}=\dfrac{\sqrt{a\cdot b}}{b}\)

\(\sqrt{\dfrac{1}{b}+\dfrac{1}{b^2}}=\dfrac{\sqrt{b+1}}{b}\)

\(\sqrt{\dfrac{9\cdot a^3}{36\cdot b}}=\dfrac{\sqrt{a^3\cdot b}}{2\cdot b}\)

\(3\cdot x\cdot y\cdot\sqrt{\dfrac{2}{x\cdot y}}=3\cdot\sqrt{2\cdot x\cdot y}\)

\(a\cdot b\cdot\sqrt{\dfrac{a}{b}}=a\cdot\sqrt{a\cdot b}\)

\(\dfrac{a}{b}\cdot\sqrt{\dfrac{b}{a}}=\dfrac{\sqrt{a\cdot b}}{b}\)

\(\sqrt{\dfrac{1}{b}+\dfrac{1}{b^2}}=\dfrac{\sqrt{b+1}}{b}\)

\(\sqrt{\dfrac{9\cdot a^3}{36\cdot b}}=\dfrac{\sqrt{a^3\cdot b}}{2\cdot b}\)

\(3\cdot x\cdot y\cdot\sqrt{\dfrac{2}{x\cdot y}}=3\cdot\sqrt{2\cdot x\cdot y}\)

a: 1/x^2y=1/x^2y

3/xy=3x/x^2y

b: \(\dfrac{x}{x^2+2xy+y^2}=\dfrac{x}{\left(x+y\right)^2}\)

\(\dfrac{2x}{x^2+xy}=\dfrac{2}{x+y}=\dfrac{2x+2y}{\left(x+y\right)^2}\)