《2025年海淀单元测试AB卷七年级数学下册沪科版》

18.(蚌埠月考)若一个正数$m$的两个平方根分别是$2a - 3$和$a - 9$，$n$是-1的立方根. 求$m - 11n$的算术平方根.

答案： 解:$\because$一个正数m的两个平方根分别是2a - 3和a - 9，$\therefore 2a - 3 + a - 9 = 0$，$\therefore a = 4$，$\therefore a - 9 = 4 - 9 = -5$，$\therefore m = (-5)² = 25$。$\because n³ = -1$，$\therefore n = -1$，$\therefore m - 11n = 25 - 11×(-1)=25 + 11 = 36$，$\therefore\sqrt{m - 11n}=\sqrt{36}=6$。

19.(1)若$a$，$b$互为相反数，$c$，$d$互为倒数，求$\sqrt[3]{a^{3} + b^{3}} + \sqrt[3]{cd} + 1$的值.
(2)若$5x + 19$的立方根是4，求$3x + 9$的平方根.

答案： 解:
(1)$\because$a，b互为相反数，$\therefore a + b = 0$。$\because$c，d互为倒数，$\therefore cd = 1$，$\therefore a + b + cd + 1 = 0 + 1 + 1 = 2$。
(2)$\because$5x + 19的立方根是4，$\therefore 5x + 19 = 4³ = 64$，解得x = 9，$\therefore 3x + 9 = 3×9 + 9 = 36$，$\therefore 3x + 9$的平方根为±6。