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1. 下列运算正确的是 (
A.$\sqrt {5^{2}-4^{2}}= \sqrt {5^{2}}-\sqrt {4^{2}}= 5-4= 1$
B.$\sqrt {(-16)(-25)}= \sqrt {-16}×\sqrt {-25}= -4×(-5)= 20$
C.$\sqrt {(\frac {5}{13})^{2}+(\frac {12}{13})^{2}}= \frac {5}{13}+\frac {12}{13}= \frac {17}{13}$
D.$\sqrt {4^{2}×7}= \sqrt {4^{2}}×\sqrt {7}= 4\sqrt {7}$
D
)A.$\sqrt {5^{2}-4^{2}}= \sqrt {5^{2}}-\sqrt {4^{2}}= 5-4= 1$
B.$\sqrt {(-16)(-25)}= \sqrt {-16}×\sqrt {-25}= -4×(-5)= 20$
C.$\sqrt {(\frac {5}{13})^{2}+(\frac {12}{13})^{2}}= \frac {5}{13}+\frac {12}{13}= \frac {17}{13}$
D.$\sqrt {4^{2}×7}= \sqrt {4^{2}}×\sqrt {7}= 4\sqrt {7}$
答案
1. D
2. 计算$(\frac {n}{m}\sqrt {\frac {m}{n}})^{2}$的结果是 (
A.1
B.$\frac {n^{2}}{m^{2}}$
C.$\frac {n}{m}$
D.$\frac {n^{3}}{m^{3}}$
C
)A.1
B.$\frac {n^{2}}{m^{2}}$
C.$\frac {n}{m}$
D.$\frac {n^{3}}{m^{3}}$
答案
2. C
3. 下列式子中,不是二次根式的是 (
A.$\sqrt {4}$
B.$\sqrt {16}$
C.$\sqrt {8}$
D.$\frac {1}{x}$
D
)A.$\sqrt {4}$
B.$\sqrt {16}$
C.$\sqrt {8}$
D.$\frac {1}{x}$
答案
3. D
4. 若$\sqrt {\frac {1}{4}a+1}$有意义,则 a 能取的最小整数为 (
A.0
B.-4
C.4
D.-8
B
)A.0
B.-4
C.4
D.-8
答案
4. B
5. 对于所有实数 a,b,下列等式总能成立的是 (
A.$(\sqrt {a}+\sqrt {b})^{2}= a+b$
B.$\sqrt {a^{2}+b^{2}}= a+b$
C.$\sqrt {(a^{2}+b^{2})^{2}}= a^{2}+b^{2}$
D.$\sqrt {(a+b)^{2}}= a+b$
C
)A.$(\sqrt {a}+\sqrt {b})^{2}= a+b$
B.$\sqrt {a^{2}+b^{2}}= a+b$
C.$\sqrt {(a^{2}+b^{2})^{2}}= a^{2}+b^{2}$
D.$\sqrt {(a+b)^{2}}= a+b$
答案
5. C
6. $\sqrt {x+1}\cdot \sqrt {x-1}= \sqrt {x^{2}-1}$成立的条件是 (
A.$x≥1$
B.$x≥-1$
C.$-1≤x≤1$
D.$x≥1或x≤-1$
A
)A.$x≥1$
B.$x≥-1$
C.$-1≤x≤1$
D.$x≥1或x≤-1$
答案
6. A
1. 使$\sqrt {x-4}$有意义的条件是
$ x \geq 4 $
.答案
1. $ x \geq 4 $
2. (1)$\sqrt {169×196}= $
(2)$\sqrt {4^{2}×3}= $
(3)$\sqrt {0.01×0.49}= $
(4)$\sqrt {3^{2}×5^{2}}= $
182
；(2)$\sqrt {4^{2}×3}= $
$ 4 \sqrt { 3 } $
；(3)$\sqrt {0.01×0.49}= $
0.07
；(4)$\sqrt {3^{2}×5^{2}}= $
15
.答案
2. (1) 182 (2) $ 4 \sqrt { 3 } $ (3) 0.07 (4) 15
3. 若$M= \sqrt {4-x}+\sqrt {x-4}+3,N= x-3$,则$M+N$的值为
4
.答案
3. 4
4. 比较大小：$\frac {1}{3}\sqrt {11}$
＜
$\frac {1}{2}\sqrt {5}$.答案
4. ＜
