計算下列各式1) 36 493

時間 2021-08-31 03:09:25

1樓:天意孤星者

1:相當於6/7的平方後再是3/2次方,就等於6/7的三次方,等於216/343

2:根號內外分別相乘,外面是18,裡面是216,216開方是6倍根號六,一起則是108倍根號6

3:底數相同,指數相加,也就是a的(1/2+1/4-1/8=5/8)次方

4:分佈運算,拆開括號,第一項是2x^(-1/3)乘以(1/2)x^(1/3)=1(任何非0的數的0次方是1),第二項2x^(-1/3)[-2x^(-2/3)]等於-4x^(-1),兩式相加得1減去4倍x的負一次方或者說1-4/x

2樓:匿名使用者

1.[√(36/49)]ˇ3=6/7ˇ3=216/3292.(√12)×(3√1.5)×(6√12)=3×6×√(12×1.5×12)=18×6√6=108√6

3. a^(1/2)a^(1/4)a^(-1/8)=aˇ(1/2+1/4-1/8)=aˇ(5/8)

4.2x^(-1/3)[(1/2)x^(1/3)-2x^(-2/3)]=2x^(-1/3)(1/2)x^(1/3)-2x^(-2/3)2x^(-1/3)=xˇ(-1/3+1/3)-4xˇ(-2/3-1/3)=1-4/x

求下列各式的值 1.25^3/2 2.27^2/3 3.(36/49)^3/2 4.(25/4)^-3/2

3樓:文奧迷

1.25^3/2=5^2*3/2=5^3=1252.27^2/3=3^3*2/3=3^2=93.(36/49)^3/2=(6/7)^2*3/2=(6/7)^3=216/343

4.(25/4)^-3/2=(5/2)^2*(-3/2)=(5/2)^-3=8/125

初二數學計算題。

4樓:我的小可愛

①5√8-2√32+√50

=5*3√2-2*4√2+5√2

=√2(15-8+5)

=12√2

②√6-√3/2-√2/3

=√6-√6/2-√6/3

=√6/6

③(√45+√27)-(√4/3+√125)

=(3√5+3√3)-(2√3/3+5√5)

=-2√5+7√5/3

④(√4a-√50b)-2(√b/2+√9a)

=(2√a-5√2b)-2(√2b/2+3√a)

=-4√a-6√2b

⑤√4x*(√3x/2-√x/6)

=2√x(√6x/2-√6x/6)

=2√x*(√6x/3)

=2/3*|x|*√6

⑥(x√y-y√x)÷√xy

=x√y÷√xy-y√x÷√xy

=√x-√y

⑦(3√7+2√3)(2√3-3√7)

=(2√3)^2-(3√7)^2

=12-63

=-51

⑧(√32-3√3)(4√2+√27)

=(4√2-3√3)(4√2+3√3)

=(4√2)^2-(3√3)^2

=32-27

=5 ⑨(3√6-√4)?

=(3√6)^2-2*3√6*√4+(√4)^2

=54-12√6+4

=58-12√6

⑩(1+√2-√3)(1-√2+√3)

=[1+(√2-√3)][1-(√2-√3)]

=1-(√2-√3)^2

=1-(2+3+2√6)

=-4-2√6

(1)5√12×√18

=5*2√3*3√2

=30√6;

(2)-6√45×(-4√48)

=6*3√5*4*4√3

=288√15;

(3)√(12a)×√(3a) /4

=√(36a^2)/4

=6a/4

=3a/2.

5. x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2

=[x(y+z)-y(x-z)]^2

=(xz+yz)^2

=z^2(x+y)^2

6. 3(a+2)^2+28(a+2)-20

=[3(a+2)-2][(a+2)+10]

=(3a+4)(a+12)

7. (a+b)^2-(b-c)^2+a^2-c^2

=(a+b)^2-c^2+a^2-(b-c)^2

=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)

=(a+b-c)(a+b+c+a-b+c)

=2(a+b-c)(a+c)

8. x(x+1)(x^2+x-1)-2

=(x^2+x)(x^2+x-1)-2

=(x^2+x)^2-(x^2+x)-2

=(x^2+x-2)(x^2+x+1)

=(x+2)(x-1)(x^2+x+1)

9. 9x^2(x-1)^2-3(x^2-x)-56

=9x^2(x-1)^2-3x(x-1)-56

=[3x(x-1)-8][3x(x-1)+7]

=(3x^2-3x-8)(3x^2-3x+7)

有理數練習

練習一(b級)

(一)計算題:

(1)23+(-73) (2)(-84)+(-49) (3)7+(-2.04) (4)4.23+(-7.

57) (5)(-7/3)+(-7/6) (6)9/4+(-3/2) (7)3.75+(2.25)+5/4 (8)-3.

75+(+5/4)+(-1.5)

5. x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2

=[x(y+z)-y(x-z)]^2

=(xz+yz)^2

=z^2(x+y)^2

6. 3(a+2)^2+28(a+2)-20

=[3(a+2)-2][(a+2)+10]

=(3a+4)(a+12)

7. (a+b)^2-(b-c)^2+a^2-c^2

=(a+b)^2-c^2+a^2-(b-c)^2

=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)

=(a+b-c)(a+b+c+a-b+c)

=2(a+b-c)(a+c)

8. x(x+1)(x^2+x-1)-2

=(x^2+x)(x^2+x-1)-2

=(x^2+x)^2-(x^2+x)-2

=(x^2+x-2)(x^2+x+1)

=(x+2)(x-1)(x^2+x+1)

9. 9x^2(x-1)^2-3(x^2-x)-56

=9x^2(x-1)^2-3x(x-1)-56

=[3x(x-1)-8][3x(x-1)+7]

=(3x^2-3x-8)(3x^2-3x+7)

1.125*3+125*5+25*3+25

2.9999*3+101*11*(101-92)

3.(23/4-3/4)*(3*6+2)

4. 3/7 × 49/9 - 4/3

5. 8/9 × 15/36 + 1/27

6. 12× 5/6 – 2/9 ×3

7. 8× 5/4 + 1/4

8. 6÷ 3/8 – 3/8 ÷6

9. 4/7 × 5/9 + 3/7 × 5/9

10. 5/2 -( 3/2 + 4/5 )

11. 7/8 + ( 1/8 + 1/9 )

12. 9 × 5/6 + 5/6

13. 3/4 × 8/9 - 1/3

14. 7 × 5/49 + 3/14

15. 6 ×( 1/2 + 2/3 )

16. 8 × 4/5 + 8 × 11/5

17. 31 × 5/6 – 5/6

18. 9/7 - ( 2/7 – 10/21 )

19. 5/9 × 18 – 14 × 2/7

20. 4/5 × 25/16 + 2/3 × 3/4

21. 14 × 8/7 – 5/6 × 12/15

22. 17/32 – 3/4 × 9/24

23. 3 × 2/9 + 1/3

24. 5/7 × 3/25 + 3/7

25. 3/14 ×× 2/3 + 1/6

26. 1/5 × 2/3 + 5/6

27. 9/22 + 1/11 ÷ 1/2

28. 5/3 × 11/5 + 4/3

29. 45 × 2/3 + 1/3 × 15

30. 7/19 + 12/19 × 5/6

31. 1/4 + 3/4 ÷ 2/3

32. 8/7 × 21/16 + 1/2

33. 101 × 1/5 – 1/5 × 21

34.50+160÷40

35.120-144÷18+35

36.347+45×2-4160÷52

37(58+37)÷(64-9×5)

38.95÷(64-45)

39.178-145÷5×6+42

40.812-700÷(9+31×11)

41.85+14×(14+208÷26)

43.120-36×4÷18+35

44.(58+37)÷(64-9×5)

45.(6.8-6.8×0.55)÷8.5

46.0.12× 4.8÷0.12×4.8

47.(3.2×1.5+2.5)÷1.6

48.6-1.6÷4= 5.38+7.85-5.37=

49.7.2÷0.8-1.2×5= 6-1.19×3-0.43=

50.6.5×(4.8-1.2×4)=

51.5.8×(3.87-0.13)+4.2×3.74

52.32.52-(6+9.728÷3.2)×2.5

53.[(7.1-5.6)×0.9-1.15] ÷2.5

54.5.4÷[2.6×(3.7-2.9)+0.62]

55.12×6÷(12-7.2)-6

56.12×6÷7.2-6

57.0.68×1.9+0.32×1.9

58.58+370)÷(64-45)

59.420+580-64×21÷28

60.136+6×(65-345÷23)

15-10.75×0.4-5.7

62.18.1+(3-0.299÷0.23)×1

63.(6.8-6.8×0.55)÷8.5

64.0.12× 4.8÷0.12×4.8

65.(3.2×1.5+2.5)÷1.6

66.3.2×6+(1.5+2.5)÷1.6

67.0.68×1.9+0.32×1.9

68.10.15-10.75×0.4-5.7

69.5.8×(3.87-0.13)+4.2×3.74

70.32.52-(6+9.728÷3.2)×2.5

71.[(7.1-5.6)×0.9-1.15] ÷2.5

72.5.4÷[2.6×(3.7-2.9)+0.62]

73.12×6÷(12-7.2)-6

74.12×6÷7.2-6

75.33.02-(148.4-90.85)÷2.5

1) 76.(25%-695%-12%)*36

77./4*3/5+3/4*2/5

78.1-1/4+8/9/7/9

79.+1/6/3/24+2/21

80./15*3/5

81.3/4/9/10-1/6

82./3+1/2)/5/6-1/3]/1/7

83./5+3/5/2+3/4

84.(2-2/3/1/2)]*2/5

85.+5268.32-2569

86.3+456-52*8

87.5%+6325

88./2+1/3+1/4

2) 89+456-78

3) 5%+. 3/7 × 49/9 - 4/3

4) 9 × 15/36 + 1/27

5) 2× 5/6 – 2/9 ×3

6) 3× 5/4 + 1/4

7) 94÷ 3/8 – 3/8 ÷6

8) 95/7 × 5/9 + 3/7 × 5/9

9) 6/2 -( 3/2 + 4/5 )

10) 8 + ( 1/8 + 1/9 )

11) 8 × 5/6 + 5/6

12) 1/4 × 8/9 - 1/3

13) 10 × 5/49 + 3/14

14) 1.5 ×( 1/2 + 2/3 )

15) 2/9 × 4/5 + 8 × 11/5

16) 3.1 × 5/6 – 5/6

17) 4/7 - ( 2/7 – 10/21 )

18) 19 × 18 – 14 × 2/7

19) 5 × 25/16 + 2/3 × 3/4

20) 4 × 8/7 – 5/6 × 12/15

21) 7/32 – 3/4 × 9/24

22) 1、 2/3÷1/2-1/4×2/5

2、 2-6/13÷9/26-2/3

3、 2/9+1/2÷4/5+3/8

4、 10÷5/9+1/6×4

5、 1/2×2/5+9/10÷9/20

6、 5/9×3/10+2/7÷2/5

7、 1/2+1/4×4/5-1/8

8、 3/4×5/7×4/3-1/2

9、 23-8/9×1/27÷1/27

10、 8×5/6+2/5÷4

11、 1/2+3/4×5/12×4/5

12、 8/9×3/4-3/8÷3/4

13、 5/8÷5/4+3/23÷9/11

23) 1.2×2.5+0.8×2.5

24) 8.9×1.25-0.9×1.25

25) 12.5×7.4×0.8

26) 9.9×6.4-(2.5+0.24)(27) 6.5×9.5+6.5×0.5

0.35×1.6+0.35×3.4

0.25×8.6×4

6.72-3.28-1.72

0.45+6.37+4.55

5.4+6.9×3-(25-2.5)2×41846-620-380

4.8×46+4.8×54

0.8+0.8×2.5

1.25×3.6×8×2.5-12.5×2.4

28×12.5-12.5×20

23.65-(3.07+3.65)

(4+0.4×0.25)8×7×1.25

1.65×99+1.65

27.85-(7.85+3.4)

48×1.25+50×1.25×0.2×8

7.8×9.9+0.78

(1010+309+4+681+6)×12

3×9146×782×6×854

5.15×7/8+6.1-0.60625

1. 3/7 × 49/9 - 4/3

2. 8/9 × 15/36 + 1/27

3. 12× 5/6 – 2/9 ×3

4. 8× 5/4 + 1/4

5. 6÷ 3/8 – 3/8 ÷6

6. 4/7 × 5/9 + 3/7 × 5/9

7. 5/2 -( 3/2 + 4/5 )

8. 7/8 + ( 1/8 + 1/9 )

9. 9 × 5/6 + 5/6

10. 3/4 × 8/9 - 1/3

11. 7 × 5/49 + 3/14

12. 6 ×( 1/2 + 2/3 )

13. 8 × 4/5 + 8 × 11/5

14. 31 × 5/6 – 5/6

15. 9/7 - ( 2/7 – 10/21 )

16. 5/9 × 18 – 14 × 2/7

17. 4/5 × 25/16 + 2/3 × 3/4

18. 14 × 8/7 – 5/6 × 12/15

19. 17/32 – 3/4 × 9/24

20. 3 × 2/9 + 1/3

21. 5/7 × 3/25 + 3/7

22. 3/14 ×× 2/3 + 1/6

23. 1/5 × 2/3 + 5/6

24. 9/22 + 1/11 ÷ 1/2

25. 5/3 × 11/5 + 4/3

26. 45 × 2/3 + 1/3 × 15

27. 7/19 + 12/19 × 5/6

28. 1/4 + 3/4 ÷ 2/3

29. 8/7 × 21/16 + 1/2

30. 101 × 1/5 – 1/5 × 21

31.50+160÷40 (58+370)÷(64-45)

32.120-144÷18+35

33.347+45×2-4160÷52

34(58+37)÷(64-9×5)

35.95÷(64-45)

36.178-145÷5×6+42 420+580-64×21÷28

37.812-700÷(9+31×11) (136+64)×(65-345÷23)

38.85+14×(14+208÷26)

39.(284+16)×(512-8208÷18)

40.120-36×4÷18+35

41.(58+37)÷(64-9×5)

42.(6.8-6.8×0.55)÷8.5

43.0.12× 4.8÷0.12×4.8

44.(3.2×1.5+2.5)÷1.6 (2)3.2×(1.5+2.5)÷1.6

45.6-1.6÷4= 5.38+7.85-5.37=

46.7.2÷0.8-1.2×5= 6-1.19×3-0.43=

47.6.5×(4.8-1.2×4)= 0.68×1.9+0.32×1.9

48.10.15-10.75×0.4-5.7

49.5.8×(3.87-0.13)+4.2×3.74

50.32.52-(6+9.728÷3.2)×2.5

51.[(7.1-5.6)×0.9-1.15] ÷2.5

52.5.4÷[2.6×(3.7-2.9)+0.62]

53.12×6÷(12-7.2)-6 (4)12×6÷7.2-6

102×4.5

7.8×6.9+2.2×6.9

5.6×0.25

8×(20-1.25)

1)127+352+73+44 (2)89+276+135+33

(1)25+71+75+29 +88 (2)243+89+111+57

9405-2940÷28×21

920-1680÷40÷7

690+47×52-398

148+3328÷64-75

360×24÷32+730

2100-94+48×54

51+(2304-2042)×23

4215+(4361-716)÷81

(247+18)×27÷25

36-720÷(360÷18)

1080÷(63-54)×80

(528+912)×5-6178

8528÷41×38-904

264+318-8280÷69

(174+209)×26- 9000

814-(278+322)÷15

1406+735×9÷45

3168-7828÷38+504

796-5040÷(630÷7)

285+(3000-372)÷36

1+5/6-19/12

3x(-9)+7x(-9

(-54)x1/6x(-1/3)

1.18.1+(3-0.299÷0.23)×1

2.(6.8-6.8×0.55)÷8.5

3.0.12× 4.8÷0.12×4.8

4.(3.2×1.5+2.5)÷1.6 (2)3.2×(1.5+2.5)÷1.6

5.6-1.6÷4= 5.38+7.85-5.37=

6.7.2÷0.8-1.2×5= 6-1.19×3-0.43=

7.6.5×(4.8-1.2×4)= 0.68×1.9+0.32×1.9

8.10.15-10.75×0.4-5.7

9.5.8×(3.87-0.13)+4.2×3.74

10.32.52-(6+9.728÷3.2)×2.5

11.[(7.1-5.6)×0.9-1.15] ÷2.5

12.5.4÷[2.6×(3.7-2.9)+0.62]

13.12×6÷(12-7.2)-6

14.12×6÷7.2-6

15.33.02-(148.4-90.85)÷2.5

7×(5/21+9/714)

a^3-2b^3+ab(2a-b)

=a^3+2a^2b-2b^3-ab^2

=a^2(a+2b)-b^2(2b+a)

=(a+2b)(a^2-b^2)

=(a+2b)(a+b)(a-b)

2. (x^2+y^2)^2-4y(x^2+y^2)+4y^2

=(x^2+y^2-2y)^2

3. (x^2+2x)^2+3(x^2+2x)+x^2+2x+3

=(x^2+2x)^2+4(x^2+2x)+3

=(x^2+2x+3)(x^2+2x+1)

=(x^2+2x+3)(x+1)^2

4. (a+1)(a+2)+(2a+1)(a-2)-12

=a^2+3a+2+2a^2-3a-2-12

=3a^2-12

=3(a+2)(a-2)

5. x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2

=[x(y+z)-y(x-z)]^2

=(xz+yz)^2

=z^2(x+y)^2

6. 3(a+2)^2+28(a+2)-20

=[3(a+2)-2][(a+2)+10]

=(3a+4)(a+12)

7. (a+b)^2-(b-c)^2+a^2-c^2

=(a+b)^2-c^2+a^2-(b-c)^2

=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)

=(a+b-c)(a+b+c+a-b+c)

=2(a+b-c)(a+c)

8. x(x+1)(x^2+x-1)-2

=(x^2+x)(x^2+x-1)-2

=(x^2+x)^2-(x^2+x)-2

=(x^2+x-2)(x^2+x+1)

=(x+2)(x-1)(x^2+x+1)

寫完一遍後再別這些題寫一遍,以此類推,老師們看作業都是一看而過不會一個一個批的。

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