Đáp án:a)\(\frac{35}{3}\sqrt{3}\)
b)\(\frac{2\sqrt{6}+3}{\sqrt{6}+2}\)
c)6
d)\(6+\sqrt{6}\)
Giải thích các bước giải:
a)\(\frac{2}{5}\sqrt{75}-0,5\sqrt{48}+\sqrt{300}-\frac{2}{3}\sqrt{12}\)
=\(\frac{2}{5}·5\sqrt{3}-0,5·4\sqrt{3}+10\sqrt{3}-\frac{2}{3}·2\sqrt{3}\)
=\(5\sqrt{3}-2\sqrt{3}+10\sqrt{3}-\frac{4}{3}\sqrt{3}=\frac{35}{3}\sqrt{3}\)
b)\(\frac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}+\frac{3}{3+\sqrt{6}}\)
=\(\frac{\sqrt{3}(3\sqrt{3}-2)}{\sqrt{2}(3\sqrt{3}-2)}+\frac{(\sqrt{3})^{2}}{\sqrt{3}(\sqrt{3}+\sqrt{2}}\)
=\(\frac{\sqrt{3}}{\sqrt{2}}+\frac{\sqrt{3}}{\sqrt{3}+\sqrt{2}}\)
=\(\frac{2\sqrt{6}+3}{\sqrt{6}+2}\)
c)\((3\sqrt{2}-2\sqrt{3})(2\sqrt{3}+3\sqrt{2})=(3\sqrt{2})^{2})-(2\sqrt{3})^{2}=18-12=6\)
d)\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
=\(\sqrt{3^{2}-2·3·\sqrt{6}+(\sqrt{6})^{2}}+\sqrt{(2\sqrt{6})^{2}+2·2·\sqrt{6}·3+3^{2}}\)
=\(\sqrt{(3-\sqrt{6})^{2}}+\sqrt{(2\sqrt{6}+3)^{2}}=|3-\sqrt{6}|+|2\sqrt{6}+3|\)
=\(3-\sqrt{6}+2\sqrt{6}+3=6+\sqrt{6}\)
