《数的开方》提高测试(9)

《数的开方》提高测试(9)
《数的开方》提高测试(9)

《数的开方》提高测试

姓名 班级 学号

(一)判断题(每小题2分,共16分)

1.两个正数,大数的平方根也较大…( ) 2.5.050050005是有理数…( ) 3.算术平方根最小的实数是0… ( )

4.因为-5的绝对值是5,所以绝对值等于5的数一定是-5…………( )

5.有理数与无理数的积是无理数( ) 6.实数中既无最大的数又无最小的数( ) 7.两个无理数的和不一定仍是无理数( )8.两个有理数之间的无理数有无数个( ) (二)填空题(每空格1分,共23分) 9.9

1

的平方根是__ _,算术平方根的相反数是_ __,算术平方根的倒数的平方根是__ _. 10.平方根等于本身的数是________;算术平方根等于本身的数是______;立方根等于

本身的数是___________. 11.如果a 2=36,那么a 3=_________.

12.如果|x |=5,那么x =_______;如果|x |=2-1,那么x =_______. 13.如果0≤a ≤1,化简|a |+|a -1|=__________. 14.当x =______时,12+x =0,当x =______时,式子2+x +2--x 有意义. 15.如果(x -6)2

+|y +2|+1+z =0,那么(x +1)2

+(y -2)2

+(z -3)2

的四次方根是______.

16.比较下列每组数的大小:

61____7

1

;0____-π;7_____2.8;-3_____-5.

17—1206科学计算器的键后,再依次按键 ________.

18.在36,2

π

,-?

?71.5,-39,38-,0.315311531115…,0中,无理数有__________

____________________;负实数有______________________;整数有________________.

19.满足-2<x <10的整数x 是______________________. 20.正方体的体积是216 cm 3,则它的表面积是_______cm 2. (三)选择题(每小题4分,共16分)

21.下列说法:①一个正数的算术平方根总比这个数小;②任何一个实数都有一个立方根,但不一定有平方根;③无限小数是无理数;④无理数与有理数的和是无理数.其中正确的是…………………………………………………………………………( )

(A )①② (B )③④ (C )①③ (D )②④ 22.a ,b 为实数,则代数式(a -b )2+ab +|a |的值…………………………( )

(A )大于0 (B )大于或等于0 (C )小于0 (D )等于0

23.一个正数的正的平方根是m ,那么比这个正数大1的数的平方根是………( )

(A )m 2+1 B .±1+m (C )12

+m (D )±12

+m

24.n 1-n

1-=2成立的条件是…………………………………………………( )

(A )n 是偶数 (B )n 是大于1的自然数 (C )n 是大于1奇数 (D )n 是整数 (四)计算题(每小题4分,共8分)

25.81.031-4162+2268101+;

26.3

008.0-+481-532-38742-.

(五)求下列各式中x 的值(每小题4分,共8分)

27.3(x 21+1)2-108=0; 28.8(x -1)3=-64125

(六)求值(每小题6分,共18分) 29.已知A =342--+b a a 是a +2的算术平方根,B =9232-+-b a b 是2-b 的立方根. 求3A -2B 的立方根.

30.已知y =12-x +x 21-+x -

2.求y x +10的值.

31.已知|x |=3,求代数式

112-x +12+x -1

1

-x 的值. (七)(6分)32.一个长方体的木箱,它的底面是正方形,木箱高0.85米,体积为1.19米3

,求这个木箱底面的边长(保留两个有效数字).

(八)(5分)33.用作图的方法在数轴上找出表示2

1

15-的点A .

《数的开方》提高测试 答案

(一)判断题(每小题2分,共16分)

1.两个正数,大数的平方根也较大 ……………………………………………(× ) 2.5.050050005是有理数…………………………………………………………( √ )

3.算术平方根最小的实数是0……………………………………………………(√ ) 4.因为-5的绝对值是5,所以绝对值等于5的数一定是-5………(× ) 5.有理数与无理数的积是无理数………………………………………………( × ) 6.实数中既无最大的数又无最小的数…………………………………………(√ ) 7.两个无理数的和不一定仍是无理数…………………………………………( √ ) 8.两个有理数之间的无理数有无数个…………………………………………(√ ) 【提示】第5题中,当有理数是零时,它与无理数的积是零,是有理数. (二)填空题(每空格1分,共23分)

9.9

1的平方根是__ _,算术平方根的相反数是_ __,算术平方根的倒数的平方根是__ _.

【答案】±

31,-3

1

,±3. 10.平方根等于本身的数是________;算术平方根等于本身的数是______;立方根等于

本身的数是___________.【答案】0;0,1;-1,0,1.

11.如果a 2=36,那么a 3

=_________.【答案】±216. 12.如果|x |=5,那么x =_______;如果|x |=2-1,那么x =_______. 【答案】±5,2-1或1-2.

13.如果0≤a ≤1,化简|a |+|a -1|=__________.【答案】1.

14.当x =______时,12+x =0,当x =______时,式子2+x +2--x 有意义.

【答案】-

2

1

,-2. 15.如果(x -6)2+|y +2|+1+z =0,那么(x +1)2+(y -2)2+(z -3)2的四次方根是______.

【答案】±3.

16.比较下列每组数的大小:

61____7

1;0____-π;7_____2.8;-3____-5.【答案】>,>,<,>.

17

—1206科学计算器的键后,再依次按键 2.

18.在36,2

π

,-?

?71.5,-39,38-,0.315311531115…,0中,无理数有

__________

____________________;负实数有______________________;整数有________________.

【答案】2

π,-3

9,0.315311531115…;-?

?71.5,-39,38-;36,38-,

0.

19.满足-2<x <10的整数x 是______________________.【答案】-1,0,1,2,3.

20.正方体的体积是216 cm 3,则它的表面积是_______cm 2.【答案】216. (三)选择题(每小题4分,共16分)

21.下列说法:①一个正数的算术平方根总比这个数小;②任何一个实数都有一个

立方根,但不一定有平方根;③无限小数是无理数;④无理数与有理数的和是无理数.其中正确的是…………………………………………………………………………( ) (A )①② (B )③④ (C )①③ (D )②④【答案】D .

22.a ,b 为实数,则代数式(a -b )2+ab +|a |的值…………………………( )

(A )大于0 (B )大于或等于0 (C )小于0 (D )等于0【答案】(B ) 23.一个正数的正的平方根是m ,那么比这个正数大1的数的平方根是………( )

(A )m 2+1 B .±1+m (C )12

+m (D )±12

+m 【答案】D .

24.n

1-n 1-=2成立的条件是…………………………………………………( ) (A )n 是偶数 (B )n 是大于1的自然数 (C )n 是大于1奇数 (D )n 是整数【答案】C .

(四)计算题(每小题4分,共8分)

25.

81.03

1-4162+2268101+;

26.3

008.0-+481-532-38742-. 【答案】25.-3.7 26.4.3.

(五)求下列各式中x 的值(每小题4分,共8分)

27.3(

x 21+1)2-108=0; 28.8(x -1)3=-

64

125

. 【答案】27.x =10或x =-14; 28.x =8

3

(六)求值(每小题6分,共18分)

29.已知A =342--+b a a 是a +2的算术平方根,B =9232-+-b a b 是2-b 的立方根.

求3A -2B 的立方根. 【提示】根据题意,得

?

?

?=-+=--39232

34b a b a 解之得

?

??==.32

b a ∴ A =2+a =22+=2,B =32b -=332-=-1.

∴ 3A -2B =3×2-2×(-1)=8. ∴ 323B A -=38=2. 【答案】2.

30.已知y =12-x +x 21-+x -

2.求y x +10的值.

【提示】根据题意,得:

??

?≥-≥-0210

12x x ∴ x =21,y =x -

2=(2

1)-2=4.

∴ y x +10=42

1

10+?=9=3.

【答案】3.

31.已知|x |=3,求代数式

112

-x +12+x -1

1

-x 的值. 【提示】∵ |x |=3.∴ x =±3.

原式=1)1()1(212-+--+x x x =1

22

--x x . 当x =3时,原式=1

)3(232

--=1323--=22

3-. 当x =-3时,原式=

1

)3(232----=

13)23(-+-=-2

2

3+.

【答案】当x =3时,原式=

223-,当x =-3时,原式=-2

2

3+. (七)(本题6分)

32.一个长方体的木箱,它的底面是正方形,木箱高0.85米,体积为1.19米3,求

这个木箱底面的边长(保留两个有效数字). 【提示】设这个木箱底面边长为x 米.

根据题意,得

0.85x 2=1.19,

x 2=1.4,

∴ x ≈1.2. 【答案】1.2米. (八)(本题5分)

33.用作图的方法在数轴上找出表示2

1

15-的点A . 【答案】如图:

点P 就是数轴上表示2

1

15-的点.

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