Đáp án+Giải thích các bước giải:

$\bullet$ 1) $\dfrac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}$

$=\dfrac{3\sqrt{2.4}-2\sqrt{4.3}+\sqrt{4.5}}{3\sqrt{9.2}-2\sqrt{9.3}+\sqrt{9.5}}$

$=\dfrac{3\sqrt{2}\sqrt{4}-2\sqrt{4}\sqrt{3}+\sqrt{4}\sqrt{5}}{3\sqrt{9}\sqrt{2}-2\sqrt{9}\sqrt{3}+\sqrt{9}\sqrt{5}}$

$=\dfrac{3.2.\sqrt{2}-2.2\sqrt{3}+2\sqrt{5}}{3.3\sqrt{2}-2.3\sqrt{3}+3\sqrt{5}}$

$=\dfrac{6\sqrt{2}-4\sqrt{3}+2\sqrt{5}}{9\sqrt{2}-6\sqrt{3}+3\sqrt{5}}$

$=\dfrac{2(3\sqrt{2}-2\sqrt{3}+\sqrt{5})}{3(3\sqrt{2}-2\sqrt{3}+\sqrt{5})}$

$=\dfrac{2}{3}$

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$\bullet$ 2) $\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+4}$

$=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{4.2}+4}{\sqrt{2}+\sqrt{3}+4}$

$=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{4}\sqrt{2}+4}{\sqrt{2}+\sqrt{3}+4}$

$=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+2\sqrt{2}+4}{\sqrt{2}+\sqrt{3}+4}$

$=\dfrac{(\sqrt{2}+\sqrt{3}+4)+\sqrt{6}+2\sqrt{2}}{\sqrt{2}+\sqrt{3}+4}$

$=\dfrac{\sqrt{2}+\sqrt{3}+4}{\sqrt{2}+\sqrt{3}+4}+\dfrac{\sqrt{6}+2\sqrt{2}}{\sqrt{2}+\sqrt{3}+4}$

$=1+\dfrac{\sqrt{6}+2\sqrt{2}}{\sqrt{2}+\sqrt{3}+4}$

Đáp án:

$\dfrac{3\sqrt8-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\\=\dfrac{3\sqrt4\sqrt2-2\sqrt4\sqrt3+\sqrt4\sqrt5}{3\sqrt9\sqrt2-2\sqrt9\sqrt3+\sqrt9\sqrt5}\\=\dfrac{6\sqrt2-4\sqrt3+2\sqrt5}{9\sqrt2-6\sqrt3+3\sqrt5}\\=\dfrac{2.(3\sqrt2-2\sqrt3+\sqrt5)}{3.(3\sqrt2-2\sqrt3+\sqrt5)}\\=\dfrac23\\\dfrac{\sqrt2+\sqrt3+\sqrt6+\sqrt8+4}{\sqrt2+\sqrt3+4}\\=\dfrac{\sqrt2+\sqrt3+4+\sqrt2\sqrt3+\sqrt4\sqrt2}{\sqrt2+\sqrt3+4}\\=\dfrac{\sqrt2+\sqrt3+4}{\sqrt2+\sqrt3+4}+\dfrac{\sqrt2\sqrt3+2\sqrt2}{\sqrt2+\sqrt3+4}\\=1+\dfrac{\sqrt2(\sqrt3+2)}{\sqrt2+\sqrt3+4}\\=1+\dfrac{2.(\sqrt3+2)}{\sqrt2(\sqrt2+\sqrt3+4)}\\=1+\dfrac{\sqrt{12}+4}{2+\sqrt6+4\sqrt2}\\=1+\dfrac{\sqrt{12}+\sqrt{16}}{2+\sqrt6+\sqrt{32}}$