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一、填空题
1. $(\sqrt{8}-\sqrt{\dfrac{9}{2}})÷\sqrt{2} =$
2. $(\sqrt{18}-\sqrt{8})×\sqrt{2} =$
3. $(\sqrt{24}+\sqrt{\dfrac{1}{6}})×\sqrt{6} =$
4. $(1-2\sqrt{3})^2 =$
5. $(5-\sqrt{3})(\sqrt{3}+2) =$
6. $(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})^2 =$
1. $(\sqrt{8}-\sqrt{\dfrac{9}{2}})÷\sqrt{2} =$
$\frac{1}{2}$
2. $(\sqrt{18}-\sqrt{8})×\sqrt{2} =$
$2$
3. $(\sqrt{24}+\sqrt{\dfrac{1}{6}})×\sqrt{6} =$
$13$
4. $(1-2\sqrt{3})^2 =$
$13-4\sqrt{3}$
5. $(5-\sqrt{3})(\sqrt{3}+2) =$
$7+3\sqrt{3}$
6. $(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})^2 =$
$\sqrt{3}-\sqrt{2}$
答案
1. $\frac{1}{2}$
2. $2$
3. $13$
4. $13-4\sqrt{3}$
5. $7+3\sqrt{3}$
6. $\sqrt{3}-\sqrt{2}$
2. $2$
3. $13$
4. $13-4\sqrt{3}$
5. $7+3\sqrt{3}$
6. $\sqrt{3}-\sqrt{2}$
二、计算题
7. $(1-2\sqrt{2})(1+2\sqrt{2})$
8. $6\sqrt{2}-2\sqrt{12}-4\sqrt{\frac{1}{8}}+3\sqrt{18}$
9. $(\frac{\sqrt{5}+2}{3})^2$
10. $\sqrt{3\frac{1}{12}} × (-\frac{1}{6}\sqrt{1\frac{5}{7}}) ÷ (\frac{1}{4}\sqrt{37})$
11. $\sqrt{24} × \sqrt{6} ÷ 3\sqrt{2} - \sqrt{\frac{1}{8}} × (1-\sqrt{2})^0$
12. $|-\sqrt{2}| + (\sqrt{2}-\frac{1}{2})^2 - (\sqrt{2}+\frac{1}{2})^2$
13. $(2\sqrt{3}-1)(\sqrt{3}+1)-(1-2\sqrt{3})^2$
14. $2\sqrt{3} × (\frac{\sqrt{2}}{2} -3 +2\sqrt{2}) ÷ \frac{1}{\sqrt{3}}$
7. $(1-2\sqrt{2})(1+2\sqrt{2})$
8. $6\sqrt{2}-2\sqrt{12}-4\sqrt{\frac{1}{8}}+3\sqrt{18}$
9. $(\frac{\sqrt{5}+2}{3})^2$
10. $\sqrt{3\frac{1}{12}} × (-\frac{1}{6}\sqrt{1\frac{5}{7}}) ÷ (\frac{1}{4}\sqrt{37})$
11. $\sqrt{24} × \sqrt{6} ÷ 3\sqrt{2} - \sqrt{\frac{1}{8}} × (1-\sqrt{2})^0$
12. $|-\sqrt{2}| + (\sqrt{2}-\frac{1}{2})^2 - (\sqrt{2}+\frac{1}{2})^2$
13. $(2\sqrt{3}-1)(\sqrt{3}+1)-(1-2\sqrt{3})^2$
14. $2\sqrt{3} × (\frac{\sqrt{2}}{2} -3 +2\sqrt{2}) ÷ \frac{1}{\sqrt{3}}$
答案
7. $-7$
8. $14\sqrt{2}-4\sqrt{3}$
9. $\frac{9+4\sqrt{5}}{9}$
10. $-\frac{2\sqrt{7}}{21}$
11. $\frac{7\sqrt{2}}{4}$
12. $-\sqrt{2}$
13. $5\sqrt{3}-8$
14. $15\sqrt{2}-18$
8. $14\sqrt{2}-4\sqrt{3}$
9. $\frac{9+4\sqrt{5}}{9}$
10. $-\frac{2\sqrt{7}}{21}$
11. $\frac{7\sqrt{2}}{4}$
12. $-\sqrt{2}$
13. $5\sqrt{3}-8$
14. $15\sqrt{2}-18$
