Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a,6\\ b,-7\\ c,\ 4\\ d,1\\ e,\ 21\sqrt{2}\\ f,\ 0\\ Bài\ 2:\\ a,\frac{\sqrt{2}}{\sqrt{7}}\\ b,\ 3\\ c,\ \frac{3\sqrt{5}}{2}\\ d,\ \frac{\sqrt{5}}{\sqrt{2}}\\ e,\ 1-\sqrt{3}\\ \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a,\ \left(\sqrt{\frac{4}{3}} +\sqrt{\frac{25}{3}} -\sqrt{3}\right)\sqrt{3} =\ \left(\frac{2}{\sqrt{3}} +\frac{5}{\sqrt{3}} -\sqrt{3}\right)\sqrt{3} =2+5-1=6\\ b,\left(\sqrt{5} +2\sqrt{3}\right)\left(\sqrt{5} -2\sqrt{3}\right) =5-4.3=-7\\ c,\ \left( 3\sqrt{2} +4\sqrt{2} -5\sqrt{2}\right)\sqrt{2} =2\sqrt{2} .\sqrt{2} =4\\ d,\ \frac{2\sqrt{5} -9\sqrt{5} +8\sqrt{5}}{\sqrt{5}} =\ \frac{\sqrt{5}}{\sqrt{5}} =1\\ e,\ 5\sqrt{2} -3\sqrt{2} +10\sqrt{2} +9\sqrt{2} =21\sqrt{2}\\ f,\ 6\sqrt{7} -10\sqrt{7} +12\sqrt{7} -8\sqrt{7} =0\\ Bài\ 2:\\ a,\ =\frac{\sqrt{2}\left(\sqrt{3} +\sqrt{5}\right)}{\sqrt{7}\left(\sqrt{3} +\sqrt{5}\right)} =\frac{\sqrt{2}}{\sqrt{7}}\\ b,\ \frac{9\sqrt{5} +9\sqrt{3}}{3\sqrt{3} +3\sqrt{5}} =\frac{9\left(\sqrt{5} +\sqrt{3}\right)}{3\left(\sqrt{3} +\sqrt{5}\right)} =3\\ c,\ \frac{\sqrt{5}\left(\sqrt{3} -1\right)}{\sqrt{3} -1} +\frac{\sqrt{5}\left(\sqrt{5} -2\right)}{2\left(\sqrt{5} -2\right)} =\sqrt{5} +\frac{\sqrt{5}}{2} =\frac{3\sqrt{5}}{2}\\ d,\ \frac{\sqrt{5}\left(\sqrt{5} -1\right)}{\sqrt{2}\left(\sqrt{5} -1\right)} =\frac{\sqrt{5}}{\sqrt{2}}\\ e,\ =1-\frac{\sqrt{3}\left(\sqrt{2} +\sqrt{3} +\sqrt{4}\right)}{\sqrt{2} +\sqrt{3} +\sqrt{4}} =1-\sqrt{3}\\ \end{array}$
