Bài 7:
a: \(\sqrt{\frac{1}{x-1}}=\sqrt{\frac{\left(x-1\right)}{\left(x-1\right)^2}}=\frac{\sqrt{x-1}}{\left|x-1\right|}\)
b: \(\sqrt{\frac{x-y}{x+y}}=\sqrt{\frac{\left(x-y\right)\left(x+y\right)}{\left.\left(x+y\right)^2\right.}}=\frac{\sqrt{x^2-y^2}}{\left|x+y\right|}\)
c: \(\sqrt{\frac{\left(x-3\right)^2}{627}}=\sqrt{\frac{627\left(x-3\right)^2}{627^2}}=\sqrt{627}\cdot\frac{\left|x-3\right|}{627}\)
d: \(\sqrt{\frac{x\sqrt{y}-y\cdot\sqrt{x}}{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}}=\sqrt{\frac{\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}}\)
\(=\sqrt{\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}}=\sqrt{\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}+\sqrt{y}\right)^2}}=\frac{\sqrt{x-y}}{\sqrt{x}+\sqrt{y}}\)
Bài 6:
a: \(\sqrt{\frac{1}{600}}=\sqrt{\frac{6}{3600}}=\frac{\sqrt6}{60}\)
b: \(\sqrt{\frac{11}{540}}=\sqrt{\frac{11}{36\cdot15}}=\sqrt{\frac{165}{36\cdot15^2}}=\frac{\sqrt{165}}{6\cdot15}=\frac{\sqrt{165}}{90}\)
e: \(ab\cdot\sqrt{\frac{a}{b}}=ab\cdot\frac{\sqrt{a}}{\sqrt{b}}=a\cdot\sqrt{ab}\)
c: \(\sqrt{\frac{3}{50}}=\sqrt{\frac{6}{100}}=\frac{\sqrt6}{10}\)
d:\(\sqrt{\frac{5}{98}}=\sqrt{\frac{10}{196}}=\frac{\sqrt{10}}{14}\)
f: \(\frac{a}{b}\cdot\sqrt{\frac{b}{a}}=\frac{a}{b}\cdot\frac{\sqrt{b}}{\sqrt{a}}=\sqrt{\frac{a}{b}}=\frac{\sqrt{ab}}{b}\)
