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\(x\sqrt{\dfrac{2}{x}}=\sqrt{x^2\cdot\dfrac{2}{x}}=\sqrt{2x}\)
\(x\sqrt{\dfrac{2}{5}}=\sqrt{\dfrac{2}{5}\cdot x^2}=\sqrt{\dfrac{2x^2}{5}}\)
\(\left(x-5\right)\cdot\sqrt{\dfrac{x}{25-x^2}}=\sqrt{\left(x-5\right)^2\cdot\dfrac{x}{-\left(x-5\right)\left(x+5\right)}}=\sqrt{-\dfrac{x\left(x-5\right)}{x+5}}\)
\(x\sqrt{\dfrac{7}{x^2}}=\sqrt{x^2\cdot\dfrac{7}{x^2}}=\sqrt{7}\)
a)\(=-\sqrt{\left(\frac{a}{b}\right)^2\cdot\frac{b}{a}}\)
\(=-\sqrt{\frac{a^2}{b^2}\cdot\frac{b}{a}}\)
\(=-\sqrt{\frac{a}{b}}\)
\(\frac{1}{2x-1}\sqrt{5-20x+20x^2}=\frac{1}{2x-1}\sqrt{5.\left(1-4x+4x^2\right)}\)
\(=\frac{1}{2x-1}\sqrt{5.\left(1-2x\right)^2}=\sqrt{\frac{1}{\left(2x-1\right)^2}}\sqrt{5.\left(2x-1\right)^2}\)(x>1/2)
\(=\sqrt{\frac{1}{\left(2x-1\right)^2}.5.\left(2x-1\right)^2}=\sqrt{5}\)
3\(\sqrt{5}\)= \(\sqrt{3^2.5}\)=\(\sqrt{45}\)
-5\(\sqrt{2}\)= \(-\sqrt{5^2.2}\)= -\(\sqrt{50}\)
\(\dfrac{-2}{3}\sqrt{xy}\) = \(-\sqrt{\left(\dfrac{2}{3}\right)^2xy}\) = -\(\sqrt{\dfrac{4}{9}xy}\)
x\(\sqrt{\dfrac{2}{x}}\)= \(\sqrt{\dfrac{2x^2}{x}}=\sqrt{2x}\)
a) \(x\sqrt{\frac{1}{x}}=\sqrt{x^2\cdot\frac{1}{x}}=\sqrt{\frac{x^2}{x}}=\sqrt{x}\)( với x > 0 )
b) \(x\sqrt{\frac{-1}{x}}=-\sqrt{x^2\cdot\frac{1}{x}}=-\sqrt{\frac{x^2}{x}}=-\sqrt{x}\)( với x < 0 )
\(\left(x-5\right)\sqrt{\frac{3}{25-x^2}}=\sqrt{\left(x-5\right)^2}\sqrt{\frac{3}{\left(5-x\right)\left(x+5\right)}}=\sqrt{\left(5-x\right)^2.\frac{3}{\left(5-x\right)\left(x+5\right)}}=\sqrt{\frac{3\left(5-x\right)}{x+5}}\)
thanks