登录
(1)在图12−1中，小正方形的边长为1，$AB = \sqrt{2}$，$BC = \sqrt{8}$，补全矩形ABCD。矩形ABCD 的面积是多少？
答案
(2)在图12−2中，小正方形的边长为1，画出矩形EFGH，使$EF = \sqrt{2}$，$FG = \sqrt{18}$。矩形EFGH的面积是多少？
答案
(1)填空:
①$\sqrt{4}×\sqrt{25} =$______，$\sqrt{4×25} =$______;
②$\sqrt{9}×\sqrt{16} =$______，$\sqrt{9×16} =$______;
③$\sqrt{(\frac{2}{3})^{2}}×\sqrt{(\frac{3}{5})^{2}} =$______，$\sqrt{(\frac{2}{3})^{2}×(\frac{3}{5})^{2}} =$______.
①$\sqrt{4}×\sqrt{25} =$______，$\sqrt{4×25} =$______;
②$\sqrt{9}×\sqrt{16} =$______，$\sqrt{9×16} =$______;
③$\sqrt{(\frac{2}{3})^{2}}×\sqrt{(\frac{3}{5})^{2}} =$______，$\sqrt{(\frac{2}{3})^{2}×(\frac{3}{5})^{2}} =$______.
答案
(2)用符号语言表示你由(1)中式子得到的猜想: ______;化简:$\sqrt{2}×\sqrt{9} =$______.
答案
(3)从右向左看(1)③中的两个式子，你有怎样的猜想？ ______;化简:$\sqrt{18} =$______.
答案
1. 下列化简过程中，正确的是 （ ）
A. $\sqrt{(-4)×(-25)} = \sqrt{-4}×\sqrt{-25} = (-2)×(-5) = 10$
B. $\sqrt{9\frac{4}{25}} = \sqrt{9}×\sqrt{\frac{4}{25}} = 3×\frac{2}{5} = \frac{6}{5}$
C. $\sqrt{27a^{4}b}(b ＞ 0) = \sqrt{3^{2}×a^{4}×3b} = 3a^{2}\sqrt{3b}$
D. $\sqrt{mn} = \sqrt{m}·\sqrt{n}$
A. $\sqrt{(-4)×(-25)} = \sqrt{-4}×\sqrt{-25} = (-2)×(-5) = 10$
B. $\sqrt{9\frac{4}{25}} = \sqrt{9}×\sqrt{\frac{4}{25}} = 3×\frac{2}{5} = \frac{6}{5}$
C. $\sqrt{27a^{4}b}(b ＞ 0) = \sqrt{3^{2}×a^{4}×3b} = 3a^{2}\sqrt{3b}$
D. $\sqrt{mn} = \sqrt{m}·\sqrt{n}$
答案
1. C
