Ta có: $\frac{2a}{2-\sqrt{a}}=\frac{2a\left(2+\sqrt{a}\right)}{\left(2-\sqrt{a}\right)\left(2+\sqrt{a}\right)}=\frac{2a\sqrt{a}+4a}{4-a}$

Đáp án cần chọn là: C

Ta có: $\frac{3}{6+\sqrt{3a}}=\frac{3\left(6-\sqrt{3a}\right)}{\left(6+\sqrt{3a}\right)\left(6-\sqrt{3a}\right)}=\frac{3\left(6-\sqrt{3a}\right)}{6^2-{\left(\sqrt{3a}\right)}^2}=\frac{3\left(6-\sqrt{3a}\right)}{36-3a}=\frac{6-\sqrt{3a}}{12-a}$

Đáp án cần chọn là: D

Ta có: $\frac{6}{\sqrt{x}+\sqrt{2y}}=\frac{6\left(\sqrt{x}-\sqrt{2y}\right)}{\left(\sqrt{x}+\sqrt{2y}\right)\left(\sqrt{x}-\sqrt{2y}\right)}=\frac{6\left(\sqrt{x}-\sqrt{2y}\right)}{x-2y}$

Đáp án cần chọn là: C

Ta có: $\frac{4}{3\sqrt{x}+2\sqrt{y}}=\frac{4\left(3\sqrt{x}-2\sqrt{y}\right)}{\left(3\sqrt{x}+2\sqrt{y}\right)\left(3\sqrt{x}-2\sqrt{y}\right)}=\frac{4\left(3\sqrt{x}-2\sqrt{y}\right)}{{\left(3\sqrt{x}\right)}^2-{\left(2\sqrt{y}\right)}^2}=\frac{12\sqrt{x}-8\sqrt{y}}{9x-4y}$

Đáp án cần chọn là: D

Ta có: $\frac{3}{2}\sqrt{6}+2\sqrt{\frac{2}{3}}-4\sqrt{\frac{3}{2}}=\frac{3}{2}\sqrt{6}+2\frac{\sqrt{6}}{3}-4\frac{\sqrt{6}}{2}=\sqrt{6}\left(\frac{3}{2}+\frac{2}{3}-\frac{4}{2}\right)=\frac{\sqrt{6}}{6}$

Đáp án cần chọn là: A

Ta có $\sqrt{\frac{3}{20}}+\sqrt{\frac{1}{60}}-2\sqrt{\frac{1}{15}}=\frac{\sqrt{3.20}}{20}+\frac{\sqrt{60}}{60}-\frac{2\sqrt{15}}{15}$

$=\frac{3\sqrt{60}+\sqrt{60}-4.\sqrt{4.15}}{60}=\frac{4\sqrt{60}-4\sqrt{60}}{60}=0$

Đáp án cần chọn là: B

$7\sqrt{x}+11y\sqrt{36x^5}-2x^2\sqrt{16x{y}^2}-\sqrt{25x}=7\sqrt{x}+11y\sqrt{6^2{x}^4.x}-2x^2\sqrt{4^{2}x{y}^2}-\sqrt{5^{2}x}$

$$\begin{gathered} =7\sqrt{x}+11y.6x^2\sqrt{x}-2x^2\mathrm{.4.}y\sqrt{x}-5\sqrt{x} \\ =7\sqrt{x}+66x^{2}y\sqrt{x}-8x^{2}y\sqrt{x}-5\sqrt{x} \end{gathered}$$

$$\begin{gathered} =\left(7\sqrt{x}-5\sqrt{x}\right)+\left(66x^{2}y\sqrt{x}-8x^{2}y\sqrt{x}\right) \\ =2\sqrt{x}+58x^{2}y\sqrt{x} \end{gathered}$$

Đáp án cần chọn là: A

$2\sqrt{\frac{16a}{3}}-3\sqrt{\frac{a}{27}}-6\sqrt{\frac{4a}{75}}=2\sqrt{4^2\frac{a}{3}}-3\sqrt{\frac{1}{9}.\frac{a}{3}}-6\sqrt{\frac{4}{25}.\frac{a}{3}}$

$$\begin{gathered} =2.4\sqrt{\frac{a}{3}}-3.\frac{1}{3}\sqrt{\frac{a}{3}}=6.\frac{2}{5}.\sqrt{\frac{a}{3}}=\sqrt{\frac{a}{3}}\left(8-1-\frac{12}{5}\right) \\ =\frac{23}{5}\sqrt{\frac{a}{3}}=\frac{23}{5}.\frac{\sqrt{3a}}{3}=\frac{23\sqrt{3a}}{15} \end{gathered}$$

Đáp án cần chọn là: A

$5\sqrt{a}+6\sqrt{\frac{a}{4}}-a\sqrt{\frac{4}{a}}+5\sqrt{\frac{4a}{25}}=5\sqrt{a}+6\sqrt{\frac{1}{4}.a}-a\sqrt{4.\frac{1}{a}}+5\sqrt{\frac{4}{25}.a}$

$=5\sqrt{a}+6\sqrt{{\left(\frac{1}{2}\right)}^2.a}-a\sqrt{2^2.\frac{1}{a}}+5\sqrt{{\left(\frac{2}{5}\right)}^2.a}=5\sqrt{a}+6.\frac{1}{2}\sqrt{a}-2a\sqrt{\frac{1}{a}}+5.\frac{2}{5}\sqrt{a}$

$=5\sqrt{a}+3\sqrt{a}-2a\frac{\sqrt{a}}{a}+2\sqrt{a}=5\sqrt{a}+3\sqrt{a}-2\sqrt{a}+2\sqrt{a}=8\sqrt{a}$

Đáp án cần chọn là: B