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1. 计算：$\sqrt{2}\times(\sqrt{2}+\sqrt{18})=$_______，$(\sqrt{12}-\sqrt{27})\div\sqrt{3}=$_______.
答案
8，-1
2. $\sqrt{7}$的整数部分等于_______，小数部分等于_______.
答案
2，$\sqrt{7}-2$
3. 已知$a = \sqrt{5}+2$，则$a^{2}-4a + 5=$_______.
答案
6
4. 若$x = \sqrt{a}-\sqrt{b}$，$y = \sqrt{a}+\sqrt{b}$，则$xy = ($ )
A. $2\sqrt{a}$
B. $2\sqrt{b}$
C. $a + b$
D. $a - b$
A. $2\sqrt{a}$
B. $2\sqrt{b}$
C. $a + b$
D. $a - b$
答案
D
5. 计算：
(1)$(2\sqrt{3}-\sqrt{6})\times\sqrt{12}$； (2)$(\sqrt{48}-\sqrt{27}+4\sqrt{15})\div\sqrt{3}$；
(3)$(2\sqrt{3}-5\sqrt{2})(\sqrt{3}-2\sqrt{2})$； (4)$(2\sqrt{3}+3\sqrt{2})(2\sqrt{3}-3\sqrt{2})$；
(5)$(2\sqrt{3}-1)^{2}$； (6)$(\frac{\sqrt{5}+1}{2})^{2}+(\frac{\sqrt{5}-1}{2})^{2}$.
(1)$(2\sqrt{3}-\sqrt{6})\times\sqrt{12}$； (2)$(\sqrt{48}-\sqrt{27}+4\sqrt{15})\div\sqrt{3}$；
(3)$(2\sqrt{3}-5\sqrt{2})(\sqrt{3}-2\sqrt{2})$； (4)$(2\sqrt{3}+3\sqrt{2})(2\sqrt{3}-3\sqrt{2})$；
(5)$(2\sqrt{3}-1)^{2}$； (6)$(\frac{\sqrt{5}+1}{2})^{2}+(\frac{\sqrt{5}-1}{2})^{2}$.
答案
(1)$12 - 6\sqrt{2}$；(2)$1 + 4\sqrt{5}$；(3)$26 - 9\sqrt{6}$；(4)-6；(5)$13 - 4\sqrt{3}$；(6)3
