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1. 求下列各式的值:
(1)$\sqrt {6^{2}}$;
(2)$-\sqrt [3]{\frac {7}{8}-1}$;
(3)$\sqrt {0.25}+\sqrt {0.36}$;
(4)$\sqrt {\frac {1}{16}}+\sqrt {0.5^{2}}-\sqrt [3]{-0.008}$.
(1)$\sqrt {6^{2}}$;
(2)$-\sqrt [3]{\frac {7}{8}-1}$;
(3)$\sqrt {0.25}+\sqrt {0.36}$;
(4)$\sqrt {\frac {1}{16}}+\sqrt {0.5^{2}}-\sqrt [3]{-0.008}$.
答案
(1)6. (2)$\frac{1}{2}$. (3)1.1. (4)0.95.
2. 求下列各式中x的值:
(1)$4x^{2}-9= 0$;
(2)$(x-2)^{3}= -0.125$.
(1)$4x^{2}-9= 0$;
$x=\pm\frac{3}{2}$
(2)$(x-2)^{3}= -0.125$.
$x=\frac{3}{2}$
答案
(1)$x=\pm\frac{3}{2}$. (2)$x=\frac{3}{2}$.
3. 求值:$(-1)^{2024}+|1-\sqrt {2}|-\sqrt [3]{8}$.
答案
解：原式$=1+\sqrt{2}-1-2=\sqrt{2}-2$.
4. 计算:$\sqrt {0.09}-\sqrt {0.36}+\sqrt {1-\frac {7}{16}}$.
答案
0.45.
5. 用计算器计算:
$\sqrt {3}+\sqrt [3]{5}-3.073$(精确到0.01).
$\sqrt {3}+\sqrt [3]{5}-3.073$(精确到0.01).
答案
0.37.
6. 已知$x-2$的算术平方根是2,$2x+y+7$的立方根是3,求$x^{2}+y^{2}$的平方根.
答案
解：由题意得$x-2=2^{2}$，$2x+y+7=3^{3}$，
$\therefore x=6$，$y=8$.
$\therefore x^{2}+y^{2}=6^{2}+8^{2}=100$.
$\therefore x^{2}+y^{2}$的平方根是$\pm10$.
$\therefore x=6$，$y=8$.
$\therefore x^{2}+y^{2}=6^{2}+8^{2}=100$.
$\therefore x^{2}+y^{2}$的平方根是$\pm10$.
