Question

Rút gọn các biểu thức sau:

a) \(\frac{y}{x}\).\(\sqrt{\frac{x^2}{y^4}}\) vơi x>0;y\(\ne\)0

b) 2y\(^2\).\(\sqrt{\frac{x^4}{4y^2}}\)  Y<0

c) 5xy.\(\sqrt{\frac{25x^2}{y^6}}\)với x<0,y>0

d) 0,2x\(^3\)y\(^3\).\(\sqrt{\frac{16}{x^4y^8}}\) với x\(\ne\)0,y\(\ne\)0

Answer 1

a/ \(\frac{y}{x}.\left(\sqrt{\frac{x^2}{y^4}}\right)=\frac{y}{x}.\frac{x}{y^2}=\frac{1}{y}\)

 

b/ \(2y^2.\sqrt{\frac{x^4}{4y^2}}=2y^2.\sqrt{\frac{\left(x^2\right)^2}{\left(-2y\right)^2}}=2y^2.\frac{x^2}{-2y}=-y.x^2\)

c/ \(5xy.\sqrt{\frac{25x^2}{y^6}}=5xy.\sqrt{\frac{\left(-5x\right)^2}{\left(y^3\right)^2}}=5xy.\frac{-5x}{y^3}=\frac{-25x^2}{y^2}\)

d/\(0,2.x^3y^3.\sqrt{\frac{4^2}{\left(x^2y^4\right)^2}}=\frac{1}{5}.x^3y^3.\frac{4}{x^2y^4}=\frac{4x}{5y}\)

 

 

 

Answer 2

Trần Việt Linh sai phần b,c,d r bn

Sửa lại:

b) 2y\(^2\).\(\sqrt{\frac{x^4}{4y^2}}\) với y<0

Ta có : 2y\(^2\).\(\sqrt{\frac{x^4}{4y^2}}\)=2y\(^2\).\(\frac{x^2}{\left|y\right|}\)

Vì y>0 nên |y| = -y.Ta có : 2y\(^2\).\(\frac{x^2}{2\left|y\right|}\)= -2y\(^2\).\(\frac{x^2}{2y}\) = -2x\(^2\)y

c) 5xy.\(\sqrt{\frac{25x^2}{y^6}}\) với x<0,y>0

Ta có :5xy\(\sqrt{\frac{25x^2}{y^6}}\)=5xy.\(\frac{5\left|x\right|}{y^3}\) ( y>0)

Vì x<0 nên |x| =-x .Ta có : 5xy.\(\frac{5\left|x\right|}{y^3}\)= -5xy.\(\frac{5x}{y^3}\) =\(\frac{-25x^2}{y^2}\)

d) 0,,2x\(^3\)y\(^3\).\(\sqrt{\frac{16}{x^4y^8}}\) với x#o,y#0

Ta có: 0,2x\(^3\)y\(^3\)\(\frac{4}{x^2y^4}\)=\(\frac{0,8x}{y}\) ( vì #0,y#0)

 

Answer 3

a)\(\frac{y}{x}\cdot\sqrt{\frac{x^2}{y^4}}=\frac{y}{x}\cdot\frac{x}{y^2}=\frac{1}{y}\)

b) \(2y^2\cdot\sqrt{\frac{x^4}{4y^2}}=2y^2\cdot\frac{x^2}{2y}=x^2y\)

c) \(5xy\cdot\sqrt{\frac{25x^2}{4y^6}}=5xy\cdot\frac{5x}{2y^3}=\frac{5x^2y}{2y^3}=\frac{5x^2}{2y^2}\)

d) \(2x^3y^3\cdot\sqrt{\frac{16}{x^4y^8}}=2x^3y^3\cdot\frac{4}{x^2y^4}=\frac{8x}{y}\)