1. 求下列各数的平方根.
(1)49； (2)$\frac {4}{25}$； (3)$\frac {1}{10^{6}}$； (4)0.0016.
(1)49； (2)$\frac {4}{25}$； (3)$\frac {1}{10^{6}}$； (4)0.0016.
答案：(1)$\pm 7$ (2)$\pm \frac {2}{5}$ (3)$\pm \frac {1}{1000}$ (4)$\pm 0.04$
2. 求x的值.
(1)$x^{2}=16$； (2)$25x^{2}-36=0$.
(1)$x^{2}=16$； (2)$25x^{2}-36=0$.
答案：解: (1)$\because x^{2}=16,\therefore x=\pm 4.$
(2)$\because 25x^{2}-36=0,\therefore 25x^{2}=36,\therefore x^{2}=\frac {36}{25},\therefore x=\pm \frac {6}{5}.$
(2)$\because 25x^{2}-36=0,\therefore 25x^{2}=36,\therefore x^{2}=\frac {36}{25},\therefore x=\pm \frac {6}{5}.$
3. 已知一个正数m的两个不同的平方根是$a-1$与$5-2a$，求a和m的值.
答案：解:$\because$一个正数$m$的两个不同的平方根是$a - 1$与$5 - 2a$,
$\therefore a - 1 + 5 - 2a = 0$, 解得$a = 4$,
$\therefore a - 1 = 3$, 故$m = 3^{2} = 9$.
$\therefore a - 1 + 5 - 2a = 0$, 解得$a = 4$,
$\therefore a - 1 = 3$, 故$m = 3^{2} = 9$.
4. 已知$2x^{2}-1=13$，求实数x的值.
答案：解:$\because 2x^{2} - 1 = 13,\therefore 2x^{2} = 14$, 即$x^{2} = 7,\therefore x = \pm \sqrt {7}$.
5. 已知$3m-1$和$m-7$是数p的平方根，求p的值.
答案：解: 当$3m - 1 = m - 7$时, 解方程$3m - 1 = m - 7$得$m = - 3$,
$\therefore 3m - 1 = - 10,\therefore p = 100$;
当$3m - 1 + m - 7 = 0$时, 解方程$3m - 1 + m - 7 = 0$得$m = 2$,
$\therefore 3m - 1 = 5,\therefore p = 25$.
$\therefore p$的值是 100 或 25.
$\therefore 3m - 1 = - 10,\therefore p = 100$;
当$3m - 1 + m - 7 = 0$时, 解方程$3m - 1 + m - 7 = 0$得$m = 2$,
$\therefore 3m - 1 = 5,\therefore p = 25$.
$\therefore p$的值是 100 或 25.
6. 已知$2a-1$的一个平方根是3，$3a+b-1$的一个平方根是-4，求$a+2b$的平方根.
答案：解:$\because 2a - 1$的一个平方根为 3,$3a + b - 1$的一个平方根为$-4,\therefore 2a - 1 = 9,3a + b - 1 = 16$, 解得$a = 5,b = 2$,
$\therefore a + 2b = 5 + 4 = 9$,
$\therefore a + 2b$的平方根为$\pm 3$.
$\therefore a + 2b = 5 + 4 = 9$,
$\therefore a + 2b$的平方根为$\pm 3$.