判断下列说法是否正确,正确的在括号内画“√”,错误的画“×”。
1. 当$a≥0,b≥0$时,$\sqrt {a}\cdot \sqrt {b}=\sqrt {ab}$. (
2. 当$a≥0,b≥0$时,$\sqrt {ab}=\sqrt {a}\cdot \sqrt {b}$. (
3. $\frac {\sqrt {a}}{\sqrt {b}}=\sqrt {\frac {a}{b}}$成立的条件是:$a≥0,b>0$. (
4. $\sqrt {\frac {a}{b}}=\frac {\sqrt {a}}{\sqrt {b}}$成立的条件是:$a≥0,b>0$. (
5. $\sqrt {(-4)×(-9)}=\sqrt {-4}×\sqrt {-9}$. (
6. $\sqrt {\frac {-9}{-25}}=\sqrt {\frac {9}{25}}=\frac {\sqrt {9}}{\sqrt {25}}=\frac {3}{5}$. (
7. $\sqrt {0.5}$是最简二次根式. (
8. $\sqrt {a^{2}+b^{2}}$是最简二次根式. (
9. $\sqrt {8a^{2}}=4a(a>0)$. (
10. $a\sqrt {-\frac {1}{a}}=\sqrt {-a}$. (
1. 当$a≥0,b≥0$时,$\sqrt {a}\cdot \sqrt {b}=\sqrt {ab}$. (
√
)2. 当$a≥0,b≥0$时,$\sqrt {ab}=\sqrt {a}\cdot \sqrt {b}$. (
√
)3. $\frac {\sqrt {a}}{\sqrt {b}}=\sqrt {\frac {a}{b}}$成立的条件是:$a≥0,b>0$. (
√
)4. $\sqrt {\frac {a}{b}}=\frac {\sqrt {a}}{\sqrt {b}}$成立的条件是:$a≥0,b>0$. (
√
)5. $\sqrt {(-4)×(-9)}=\sqrt {-4}×\sqrt {-9}$. (
×
)6. $\sqrt {\frac {-9}{-25}}=\sqrt {\frac {9}{25}}=\frac {\sqrt {9}}{\sqrt {25}}=\frac {3}{5}$. (
√
)7. $\sqrt {0.5}$是最简二次根式. (
×
)8. $\sqrt {a^{2}+b^{2}}$是最简二次根式. (
√
)9. $\sqrt {8a^{2}}=4a(a>0)$. (
×
)10. $a\sqrt {-\frac {1}{a}}=\sqrt {-a}$. (
×
)答案
1. √;2. √;3. √;4. √;5. ×;6. √;7. ×;8. √;9. ×;10. ×
1. 二次根式$\sqrt {(-2)^{2}×6}$的计算结果是 (
A. $2\sqrt {6}$
B. $-2\sqrt {6}$
C. 6
D. 12
A
)A. $2\sqrt {6}$
B. $-2\sqrt {6}$
C. 6
D. 12
答案
A
2. 若$\frac {\sqrt {a^{2}}}{\sqrt {b^{2}}}=-\frac {a}{b}$,则 (
A. $a<0,b<0$
B. $a>0,b>0$
C. $ab>0$
D. $ab≤0$且$b≠0$
D
)A. $a<0,b<0$
B. $a>0,b>0$
C. $ab>0$
D. $ab≤0$且$b≠0$
答案
D
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