Question

6. Đưa thừa số vào trong dấu căn :
a) x * sqrt(y/x)
b) x/y * sqrt(y/x)

Answer 1

a.

- Nếu \(\left\{{}\begin{matrix}x>0\\y\ge0\end{matrix}\right.\) \(\Rightarrow x\sqrt{\dfrac{y}{x}}=\sqrt{x^2.\dfrac{y}{x}}=\sqrt{xy}\)

- Nếu \(\left\{{}\begin{matrix}x< 0\\y< 0\end{matrix}\right.\) \(\Rightarrow x\sqrt{\dfrac{y}{x}}=-\sqrt{x^2.\dfrac{y}{x}}=-\sqrt{xy}\)

b.

ĐKXĐ: \(\dfrac{y}{x}>0\)

\(\dfrac{x}{y}.\sqrt{\dfrac{y}{x}}=\sqrt{\left(\dfrac{x}{y}\right)^2.\dfrac{y}{x}}=\sqrt{\dfrac{x}{y}}\)