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1. 计算:
(1)$(\sqrt{6}-\sqrt{\frac{3}{8}})\times\sqrt{2}$； (2)$(2+\sqrt{2})(1-\sqrt{2})$;
(3)$(\sqrt{2}+1)(\sqrt{2}-1)$； (4)$(\sqrt{2}-\sqrt{3})^{2}$.
(1)$(\sqrt{6}-\sqrt{\frac{3}{8}})\times\sqrt{2}$； (2)$(2+\sqrt{2})(1-\sqrt{2})$;
(3)$(\sqrt{2}+1)(\sqrt{2}-1)$； (4)$(\sqrt{2}-\sqrt{3})^{2}$.
答案
2. 计算:
(1)$a\sqrt{16a}+3\sqrt{a^{3}}-\frac{1}{2}a\sqrt{\frac{4}{a}}(a＞0)$； (2)$(2+\sqrt{5})(3 - 2\sqrt{5})$;
(3)$(3\sqrt{2}+\sqrt{7})(3\sqrt{2}-\sqrt{7})$； (4)$(\sqrt{5}-\sqrt{10})^{2}$.
(1)$a\sqrt{16a}+3\sqrt{a^{3}}-\frac{1}{2}a\sqrt{\frac{4}{a}}(a＞0)$； (2)$(2+\sqrt{5})(3 - 2\sqrt{5})$;
(3)$(3\sqrt{2}+\sqrt{7})(3\sqrt{2}-\sqrt{7})$； (4)$(\sqrt{5}-\sqrt{10})^{2}$.
答案
3. 计算:
(1)$(\frac{-1+\sqrt{3}}{2})^{2}$； (2)$(\frac{-1-\sqrt{5}}{2})^{2}$.
(1)$(\frac{-1+\sqrt{3}}{2})^{2}$； (2)$(\frac{-1-\sqrt{5}}{2})^{2}$.
答案
4. 已知菱形的两条对角线长分别为$(4+\sqrt{3})\text{ cm}$、$(4-\sqrt{3})\text{ cm}$，求该菱形的面积.
答案
5. 已知$x=\sqrt{3}+1$，$y=\sqrt{3}-1$，求下列各式的值:
(1)$x^{2}+2xy + y^{2}$； (2)$x^{2}-y^{2}$.
(1)$x^{2}+2xy + y^{2}$； (2)$x^{2}-y^{2}$.
答案
