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problems on cube roots and cubes

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The following table describes the cubes of the numbers. The first column represents the number. Second column represents the cube . the third column represents the last digit of the cube. The fourth column represents the sum of the digits of the cube.By observing the table we can observe many things. The sum of the digits in the cube are 1,8,9. If we see the last column 1,8,9 are repeating every time. Yes it is a great magic on cubes.
              If we observe the column number three,which is the sum of the digits in a cube, the series follows 1,8,7,4,5,6,3,2,9,0. For every 10 cubes the same sequence is following. So this is a great magic. 


Number
Cube of a number
Last digit in the number
Sum of the digits
in the cube
1
1
1
1
2
8
8
8
3
27
7
9
4
64
4
1
5
125
5
8
6
216
6
9
7
343
3
1
8
512
2
8
9
729
9
9
10
1000
0
1
11
1331
1
8
12
1728
8
9
13
2197
7
1
14
2744
4
8
15
3375
5
9
16
4096
6
1
17
4913
3
8
18
5832
2
9
19
6859
9
1
20
8000
0
8
21
9261
1
9
22
10648
8
1
23
12167
7
8
24
13824
4
9
25
15625
5
1
26
17576
6
8
27
19683
3
9
28
21952
2
1
29
24389
9
8
30
27000
0
9
31
29791
1
1
32
32768
8
8
33
35937
7
9
34
39304
4
1
35
42875
5
8
36
46656
6
9
37
50653
3
1
38
54872
2
8
39
59319
9
9
40
64000
0
1
41
68921
1
8
42
74088
8
9
43
79507
7
1
44
85184
4
8
45
91125
5
9
46
97336
6
1
47
103823
3
8
48
110592
2
9
49
117649
9
1
50
125000
0
8


By observing the above table we can write the following table
Number
10
20
30
40
50
60
70
80
90
100
Cube
1000
8000
27000
640000
125000
216000
343000
512000
729000
100000

By observing the above table
1.       If the cube is below 1000 then the number is below 10
2.       If the cube is between 1000 to 8000, then the number is between 11 to 20.
3.       If the cube is between 8001 to 27000, then the number isbetween 21 to 30
4.       If the cube is between 27001 to 64000, then the number is between 31 to 40
5.       If the cube is between 64001 to 125000, then the number is between 41 to 50.
6.       If the cube is between 125001 to 216000, then the number is between 51 to 60.
7.       If the cube is between 216000 to 343001, then the number is between 61 to 70.
8.       If the cube is between 343001 to 512000, then the number is between 71 to 80.
9.       If the cube is between 512001 to 729000, then the number is between 81 to 90.
10.   If the cube is between 729001 to 100000, then the number is between 91 to 100.

Number(last digit in number)
Last digit in cube
Easy identification for number(last digit in number)

1
1
1

2
8
2(10-8)

3
7
3(10-7)

4
4
4

5
5
5

6
6
6

7
3
7(10-3)

8
2
8(10-2)

9
9
9

10
0
0


By seeing the above table when the last digit in the cube is 1,4,5,6,9,0 the the last digit in the cube root also same. But when the last digit in the cube is 2,3,8,7 then subtract these digits from 10, then the last digit in cuberoot number will appear.
Now we will see for the cube related problems.
1.cube of a number is 15625. Then what is that number.
Sol: step 1: cube of a number is 15625.
        Step2: last in the cuberoot number is 5
        Step3: 15625 lies between 8001 to 27000, then cube root lies between 20 to 30
       Step4:  then the cube root is 25.

2.cube of a number is 32768. Then what is that number.
Sol: Sol: step 1: cube of a number is 32768.
        Step2: last  digit in the cube is 8. Then last digit in the cuberoot is 2
        Step3: 32768 lies between 27000 to 64000, then cube root lies between 30 to 40
       Step4:  then the cube root is 32.

3.cube of a number is 32768. Then what is that number.
Sol: Sol: step 1: cube of a number is 21952.
        Step2: last  digit in the cube is 2. Then last digit in the cuberoot is 8
        Step3: 32768 lies between 8000 to 27000, then cube root lies between 20 to 30
       Step4:  then the cube root is 28.
4.cube of a number is 32768. Then what is that number.
Sol: Sol: step 1: cube of a number is 32768.
        Step2: last  digit in the cube is 8. Then last digit in the cuberoot is 2
        Step3: 32768 lies between 27000 to 64000, then cube root lies between 30 to 40
       Step4:  then the cube root is 32.
5.cube of a number is 35937. Then what is that number.
Sol: Sol: step 1: cube of a number is 35937.
        Step2: last  digit in the cube is 7. Then last digit in the cuberoot is 3
        Step3: 35937 lies between 27000 to 64000, then cube root lies between 30 to 40.
        Step4:  then the cube root is 33.

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