\(=\sqrt{\left(\dfrac{2\sqrt{5}+2}{3-\sqrt{5}}\right)^2\cdot\dfrac{24-8\sqrt{5}}{3+3\sqrt{5}}}\)

\(=\sqrt{\left(36+16\sqrt{5}\right)\cdot\dfrac{-16+8\sqrt{5}}{3}}\)

\(=\sqrt{\dfrac{64+32\sqrt{5}}{3}}\)

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\(\sqrt{\dfrac{2}{x}}\)= \(\sqrt{\dfrac{2x^2}{x}}=\sqrt{2x}\)

\(3\sqrt{5}=\sqrt{45}\)

\(x\sqrt{\dfrac{2}{x}}=\sqrt{x^2\cdot\dfrac{2}{x}}=\sqrt{2x}\)

\(x\sqrt{\dfrac{2}{5}}=\sqrt{\dfrac{2}{5}\cdot x^2}=\sqrt{\dfrac{2x^2}{5}}\)

\(\left(x-5\right)\cdot\sqrt{\dfrac{x}{25-x^2}}=\sqrt{\left(x-5\right)^2\cdot\dfrac{x}{-\left(x-5\right)\left(x+5\right)}}=\sqrt{-\dfrac{x\left(x-5\right)}{x+5}}\)

\(x\sqrt{\dfrac{7}{x^2}}=\sqrt{x^2\cdot\dfrac{7}{x^2}}=\sqrt{7}\)

Bài 1: Đưa thừa số ra ngoài dấu căn:

\(2\sqrt{225a^2}=2.15a=30a\)

Bài 2: Đưa thừa số vào trong dấu căn :

\(x\sqrt{\dfrac{-39}{x}}=\sqrt{x^2.\dfrac{-39}{x}}=\sqrt{-39x}\)

Bài 3: Sắp xếp theo thứ tự tăng dần :

a) \(2\sqrt{3}< 3\sqrt{2}< 2\sqrt{5}< 5\sqrt{2}\)

b) \(4\sqrt{2}< \sqrt{37}< 2\sqrt{15}< 3\sqrt{7}\)

c) \(6\sqrt{\dfrac{1}{3}}< \sqrt{27}< 2\sqrt{28}< 5\sqrt{7}\)

Bài 2: 

\(\dfrac{2\sqrt{3}-10}{5}\cdot\sqrt{\dfrac{5+\sqrt{3}}{5-\sqrt{3}}}\)

\(=\dfrac{2\sqrt{3}-10}{5}\cdot\sqrt{\dfrac{28+10\sqrt{3}}{22}}\)

\(=\dfrac{2\sqrt{3}-10}{5}\cdot\dfrac{5+\sqrt{3}}{\sqrt{22}}\)

\(=\dfrac{2\left(\sqrt{3}-5\right)\left(\sqrt{3}+5\right)}{5\sqrt{22}}\)

\(=\dfrac{2\cdot\left(3-25\right)}{5\sqrt{22}}=\dfrac{-44}{5\sqrt{22}}=\dfrac{-2\sqrt{22}}{5}\)

\(3\sqrt{5}=\sqrt{45}\)

\(-5\sqrt{2}=-\sqrt{25}.\sqrt{2}=-\sqrt{50}\)

\(\dfrac{-2}{3}\sqrt{xy}=-\sqrt{\dfrac{4}{9}}.\sqrt{xy}=-\sqrt{\dfrac{4}{9}xy}\left(xy\ge0\right)\)

\(x\sqrt{\dfrac{2}{x}}=\sqrt{x^2}.\sqrt{\dfrac{2}{x}}=\sqrt{\dfrac{2x^2}{x}}=\sqrt{2x}\left(x>0\right)\)