1. 当$x$____时,$\sqrt {4-x}$在实数范围内有意义.
答案:
≤4
2. 在$\sqrt {3},\sqrt {-14},\sqrt {a^{2}+1},\sqrt {b},\sqrt [3]{x^{2}}$中,是二次根式的是____.
答案:
$\sqrt{3}$,$\sqrt{a^{2}+1}$
3. 当$x$____时,$\sqrt {x-8}$是二次根式.
答案:
≥8
4. 当$x$____时,等式$\sqrt {\frac {x-1}{x+1}}= \frac {\sqrt {x-1}}{\sqrt {x+1}}$成立.
答案:
≥1
5. 计算:$\sqrt {2a^{2}bc}÷\sqrt {8ac}= $____,$\frac {\sqrt {5xy}}{\sqrt {x^{3}y}}= $____$(x>0,y>0)$.
答案:
$\frac{\sqrt{ab}}{2}$ $\frac{\sqrt{5}}{x}$
6. 要使二次根式$\sqrt {x+1}$有意义,$x$必须满足的条件是()
A.$x≥1$
B.$x>-1$
C.$x≥-1$
D.$x>1$
A.$x≥1$
B.$x>-1$
C.$x≥-1$
D.$x>1$
答案:
C
7. 下列结论中,正确的是()
A.$\sqrt {(-3)^{2}}= -3$
B.$(-\sqrt {5})^{2}= -5$
C.$-\sqrt {(-3)^{2}}= -3$
D.$-\sqrt {(-7)^{2}}= 7$
A.$\sqrt {(-3)^{2}}= -3$
B.$(-\sqrt {5})^{2}= -5$
C.$-\sqrt {(-3)^{2}}= -3$
D.$-\sqrt {(-7)^{2}}= 7$
答案:
C
8. 给出下面四个算式:①$3\sqrt {2}×4\sqrt {2}= 12\sqrt {2}$;②$5\sqrt {x}\cdot 5\sqrt {y}= 5\sqrt {xy}$;③$2\sqrt {\frac {y}{x}}\cdot 3\sqrt {\frac {x}{y}}= 6$;④$\sqrt {(-7)^{2}×5}= -7\sqrt {5}$.其中正确算式的个数是()
A.0
B.1
C.2
D.3
A.0
B.1
C.2
D.3
答案:
B
9. 若$x+|x-1|= 1$,则化简$\sqrt {(x-1)^{2}}+\sqrt {(2-x)^{2}}$的结果是()
A.$3-2x$
B.1
C.-1
D.$2x-3$
A.$3-2x$
B.1
C.-1
D.$2x-3$
答案:
A
10. 已知$y= \sqrt {2x-5}+\sqrt {5-2x}-3$,则$2xy$的值为()
A.-15
B.15
C.$-\frac {15}{2}$
D.$\frac {15}{2}$
A.-15
B.15
C.$-\frac {15}{2}$
D.$\frac {15}{2}$
答案:
A
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