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Đáp án+Giải thích các bước giải:

 `a)`

`5\sqrt{a}-3\sqrt{25a^{3}}+2\sqrt{36ab^{2}}-2\sqrt{9a}` `(a>0;b>0)`

`=5\sqrt{a}-3.\sqrt{(5a)^{2}.a}+2\sqrt{(6b)^{2}.a}-2\sqrt{3^{2}.a}`

`=5\sqrt{a}-3.5a\sqrt{a}+2.6b.\sqrt{a}-2.3\sqrt{a}`

`=5\sqrt{a}-15a\sqrt{a}+12b\sqrt{a}-6\sqrt{a}`

`=12b\sqrt{a}-15a\sqrt{a}-\sqrt{a}`

`=\sqrt{a}.(12b-15a-1)`

`b)`

`\sqrt{64ab^{3}}-3\sqrt{12a^{3}b^{3}}+2ab.\sqrt{9ab}-5b\sqrt{81a^{3}b}` `(a>0;b>0)`

`=\sqrt{(8b)^{2}.ab}-3.\sqrt{2^{2}.3.(ab)^{2}.ab}+2ab.\sqrt{3^{2}.ab}-5b.\sqrt{(9a)^{2}.ab}`

`=8b\sqrt{ab}-3.\sqrt{12}.ab.\sqrt{ab}+2ab.3\sqrt{ab}-5b.9a.\sqrt{ab}`

`=8b\sqrt{ab}-3.2\sqrt{3}ab\sqrt{ab}+6ab\sqrt{ab}-45ab\sqrt{ab}`

`=\sqrt{ab}.(8b-6\sqrt{3}ab+6ab-45ab)`

`=\sqrt{ab}.(8b-39ab-6\sqrt{3}ab)`

`c)`

`2\sqrt{3a}-\sqrt{75a}+a.\sqrt{\frac{13,5}{2a}}-2/5\sqrt{300a^{3}}` `(a>0;b>0)`

`=2\sqrt{3a}-\sqrt{5^{2}.3a}+\sqrt{\frac{13,5a^{2}}{2a}}-2/5.\sqrt{(10a^{2}).3a}`

`=2\sqrt{3a}-5\sqrt{3a}+\sqrt{\frac{13,5a}{2}}-2/5. 10a\sqrt{3a}`

`=-3\sqrt{3a}+\frac{\sqrt{13,5}}{\sqrt{2}}.\sqrt{a}-20/5a\sqrt{3a}`

`=-3\sqrt{3a}+\frac{3\sqrt{3}}{2}.\sqrt{a}-4a\sqrt{3a}`

`=\sqrt{3a}.(-3+3/2-4a)`

`=\sqrt{3a}.(-3/2-\frac{8a}{2})`

`=\sqrt{3a}.\frac{-3-8a}{2}`

`=\frac{(-3-8a).\sqrt{3a}}{2}`

`=\frac{-3\sqrt{3a}-8a\sqrt{3a}}{2}`