a) \(\dfrac{y}{x}\cdot\sqrt{\dfrac{x^2}{y^4}}\)
\(=\dfrac{y}{x}\cdot\dfrac{\sqrt{x^2}}{\sqrt{\left(y^2\right)^2}}\)
\(=\dfrac{y}{x}\cdot\dfrac{x}{y^2}\)
\(=\dfrac{1}{y}\)
b) \(\dfrac{5}{2}x^3y^3\cdot\sqrt{\dfrac{16}{x^4y^8}}\)
\(=\dfrac{5}{2}x^3y^3\cdot\dfrac{\sqrt{16}}{\sqrt{\left(x^2y^4\right)^2}}\)
\(=\dfrac{5}{2}x^3y^3\cdot\dfrac{4}{x^2y^4}\)
\(=\dfrac{20x^3y^3}{2x^2y^4}\)
\(=\dfrac{10x}{y}\)
c) \(ab^2\sqrt{\dfrac{3}{a^2b^4}}\)
\(=ab^2\dfrac{\sqrt{3}}{\sqrt{\left(ab^2\right)^2}}\)
\(=ab^2\cdot\dfrac{\sqrt{3}}{ab^2}\)
\(=\sqrt{3}\)
\(a,\dfrac{y}{x}\cdot\sqrt{\dfrac{x^2}{y^4}}\left(y\ge0;x,y\ne0\right)\) (sửa đề)
\(=\dfrac{y}{x}\cdot\dfrac{\sqrt{x^2}}{\sqrt{y^4}}\)
\(=\dfrac{y}{x}\cdot\dfrac{x}{\sqrt{\left(y^2\right)^2}}\)
\(=\dfrac{y}{x}\cdot\dfrac{x}{y^2}\)
\(=\dfrac{1}{y}\)
\(---\)
\(b,\dfrac{5}{2}x^3y^3\cdot\sqrt{\dfrac{16}{x^4y^8}}\left(x,y\ne0\right)\)
\(=\dfrac{5}{2}x^3y^3\cdot\dfrac{\sqrt{16}}{\sqrt{x^4y^8}}\)
\(=\dfrac{5x^3y^3}{2}\cdot\dfrac{4}{x^2y^4}\)
\(=\dfrac{5x\cdot2}{y}\)
\(=\dfrac{10x}{y}\)
\(---\)
\(c,ab^2\sqrt{\dfrac{3}{a^2b^4}}\left(a>0;b\ne0\right)\) (sửa đề)
\(=ab^2\cdot\dfrac{\sqrt{3}}{\sqrt{a^2b^4}}\)
\(=\dfrac{ab^2\sqrt{3}}{\sqrt{\left(ab^2\right)^2}}\)
\(=\dfrac{ab^2\sqrt{3}}{ab^2}\)
\(=\sqrt{3}\)
#\(Toru\)
