利用多维数据集根表,找到以下多维数据集根(正确到小数点后三位):
问题1. 7
解决方案:
We know that 7 lies between 1-100 so using cube root table we will get ∛7 = 1.913
问题2. 70
解决方案:
We know that 70 lies between 1-100 so using cube root table we will get ∛70 = 4.121
问题3. 700
解决方案:
We can write 700 as 70×10
Now we can write ∛700 as ∛70 x ∛10 and we will get ∛700 = 8.879
问题4. 7000
解决方案:
We can write 7000 as 70×100
Now we can write ∛7000 as ∛7 × ∛1000
Using cube root table and we get ∛7 = 1.913 and ∛1000 = 10
= 1.913 × 10 = 19.13
问题5.1100
解决方案:
We can write 1100 as 11 x 100
Now we can write ∛1100 as ∛11 × ∛100
Using cube root table we get ∛11 = 2.224 and ∛100 = 4.6642
= 2.224 × 4.642 = 10.323
问题6. 780
解决方案:
We can write 780 as 78×10
We can write ∛780 as ∛78 and ∛10
Using cube root table we get ∛78 = 4.272 and ∛10 = 2.154
= 4.272 x 2.154 = 9.205
问题7. 7800
解决方案:
We can write 7800 as 78×100
Now we can write ∛7800 as ∛78 × ∛100
Using cube root table we get ∛78 = 4.273 and ∛100 = 4.6642
= 4.273 × 4.642 = 19.835
问题8. 1346
解决方案:
Let’s find the factors of 1346 and we can write it as 2×673
Now we can write ∛1346 as ∛2 × ∛673
Since 673 lies between 670 & 680 so ∛670 < ∛673 < ∛680
Now using cube root table we get
∛670 = ∛67 x ∛10 = 8.750
∛680 = ∛68 x ∛10 = 8.794
Difference between 680 & 670 is 10.
So the difference in their cube roots are : 8.794 – 8.750 = 0.044
Difference between 673 & 670 is 3.
So the difference in their cube will : (0.044/10) × 3 = 0.0132
∛673 = 8.750 + 0.013 = 8.763
We can write ∛1346 as ∛2 × ∛673
= 1.260 × 8.763 = 11.041
问题9. 250
解决方案:
We can write 250 as 25×100 and further ∛25 x ∛10
We get 6.3
问题10.5112
解决方案:
Let’s find the factor of 5112,
We get ∛(2×2×2×3×3×71)
= 2 × ∛9 × ∛71
Using cube root table we get ∛9 = 2.080 & ∛71 = 4.141
= 2 × 2.080 × 4.141 = 17.227
问题11. 9800
解决方案:
We can write ∛9800 as ∛98 × ∛100
Using cube root table we get ∛98 = 4.610 & ∛100 = 4.642
= 4.610 × 4.642 = 21.40
问题12.732
解决方案:
As we know that the value of ∛732 will lie between ∛730 & ∛740
Using cube root table we get ∛730 = 9.004 & ∛740 = 9.045
Now we will use unitary method,
Difference between 740 & 730: (740 – 730) = 10
So the difference between their cube roots will be : 9.045 – 9.004 = 0.041
Difference between the values: 732 – 730 = 2
Now we will calculate difference in cube root values: (0.041/10) ×2 = 0.008
∛732 = 9.004+0.008 = 9.012
问题13:7342
解决方案:
As we know that the value of ∛7342 will lie between ∛7300 & ∛7400
Using cube root table we will get ∛7300 = 19.39 & ∛7400 = 19.48
Now we will use unitary method,
Difference between 7400 & 7300 = 100
So the difference between their cube roots will be : 19.48 – 19.39 = 0.09
Difference between the values : 7342 – 7300 = 42
Now we will calculate difference in cube root values : (0.09/100) × 42 = 0.037
∛7342 = 19.39+0.037 = 19.427
问题14.133300
解决方案:
We can write ∛133100 as ∛ 1331 × ∛ 100,
= 11 × ∛100
Using cube root table we get ∛100 = 4.462
= 11 × 4.462 = 51.062
问题15. 37800
解决方案:
Let us find the factors for 37800
We get ∛(2×2×2×3×3×3×175)
= 2 x 3 x ∛(175)
= 6 × ∛175
As we know that the value of ∛175 will lie between ∛170 & ∛180
Using cube root table we get ∛170 = 5.540 & ∛180 = 5.646
Now we will use Unitary method,
Difference between 180 & 170 = 10
So the difference between their cube roots will be : 5.646 – 5.540 = 0.106
Difference between the values 175 & 170 = 5
So the difference in their cube roots will be = (0.106/10) × 5 = 0.053
∛175 = 5.540 + 0.053 = 5.593
∛37800 = 6 × ∛175 = 6 × 5.593 = 33.558
问题16. 0.27
解决方案:
We can write ∛0.27 as ∛27/∛100
By using cube root table we get ∛27 = 3 & ∛100 = 4.642
∛0.27 = ∛27/∛100
= 3/4.642 = 0.646
问题17. 8.6
解决方案:
∛8.6 = ∛86/∛10
By using cube root table we get ∛86 = 4.414 & ∛10 = 2.154
∛8.6 = ∛86/∛10
= 4.414/2.154 = 2.049
问题18.0.86
解决方案:
∛0.86 = ∛86/∛100
By using cube root table we get ∛86 = 4.414 & ∛100 = 4.642
∛8.6 = ∛86/∛100
= 4.414/4.642 = 0.9508
问题19.8.65
解决方案:
∛8.65 = ∛865/∛100
As we know that value of ∛865 will lie between ∛860 & ∛870
Using cube root table we get ∛860 = 9.510 & ∛870 = 9.546 & ∛100 = 4.642
We will use Unitary method,
Difference between the values 870 & 860 = 10
So, the difference in their cube roots will be : 9.546 – 9.510 = 0.036
Difference between the values 865 – 860 = 5
So, the difference between their cube roots will be : (0.036/10) × 5 = 0.018
∛865 = 9.510 + 0.018 = 9.528
∛8.65 = ∛865/∛100
= 9.528/4.642 = 2.0525
问题20. 7532
解决方案:
As we know that value of ∛7532 will lie between ∛7500 & ∛7600
Using cube root table we get ∛7500 = 19.57 & ∛7600 = 19.66
Now we will use Unitary method,
Difference between the values 7600 & 7500 : 7600 – 7500 = 100
So the difference between their cube roots will :19.66 – 19.57 = 0.09
Difference between the values 7532 – 7500 = 32
So the difference between their cube root will : (0.09/100) × 32 = 0.029
∛7532 = 19.57 + 0.029 = 19.599
问题21. 833
解决方案:
As we know that value of ∛833 will lie between ∛830 and ∛840
Using cube root table we get ∛830 = 9.398 & ∛840 = 9.435
We will use Unitary method,
Difference between the values 840 & 830 = 840 – 830 = 10
So, the difference in their cube root values will be : 9.435 – 9.398 = 0.037
Difference between the values 833 & 830 = 3
So, the difference in their cube root values will be = (0.037/10) ×3 = 0.011
∛833 = 9.398+0.011 = 9.409
问题22. 34.2
解决方案:
∛34.2 = ∛342/∛10
As we know that value of ∛342 will lie between ∛340 & ∛350
Using cube root table we get ∛340 = 6.980 & ∛350 = 7.047 & ∛10 = 2.154
We will use Unitary method,
Difference between the values 350 & 340 = 10
So, the difference in cube root values will be : 7.047 – 6.980 = 0.067
Difference between the values 342 & 340 = 2
So, the difference in their cube root values will be = (0.067/10) × 2 = 0.013
∛342 = 6.980 + 0.013 = 6.993
∛34.2 = ∛342/∛10
= 6.993/2.154 = 3.246
问题23.体积为275 cm 3的立方体的边长是多少。利用该表作为多维数据集的根。
解决方案:
Given that,
Volume of the cube = 275cm3
Let us assume that the side of the cube as ‘a’ cm
As we know that Volume of Cube : a^3 = 275
a = ∛275
Now we know that the value of ∛275 will lie between ∛270 & ∛280
Using cube root table we get ∛270 = 6.463 & ∛280 = 6.542
We will use Unitary method,
Difference between the values 280 & 270 = 10
So the difference in their cube root will = 6.542 – 6.463 = 0.079
Difference between the values 275 & 270 = 5
So the difference in their cube roots will be = (0.079/10) × 5 = 0.0395
∛275 = 6.463 + 0.0395 = 6.5025