Cube roots of perfect cubes

Here are eight poets, namely, A, B, C, D, E, F, G and H in respect of whom questions are being asked in the examination. The first four are ancient poets and the last four are modern poets. The question on ancient and modern poets is being asked in alternate years. Those who like H also like G, those who like D like C also. The examiner who sets question is not likely to ask question on D because he has written an article on him. But he likes D. Last year a question was asked on F. Considering these facts, on whom the question is most likely to be asked this year? 

a. B
b. C
c. D
d. G

Points to remember  for speedy  calculation of cube roots of perfect cubes

1. To calculate cube root of any perfect cube quickly, we need to remember the cubes of 1 to 10 which is given below.

1³	=	1
2³	=	8
3³	=	27
4³	=	64
5³	=	125
6³	=	216
7³	=	343
8³	=	512
9³	=	729
10³	=	1000

2. From the above cubes of 1 to 10, we need to remember an interesting property.

1³	=	1	=>	If the last digit of the perfect cube = 1, the last digit of the cube root = 1
2³	=	8	=>	If the last digit of the perfect cube = 8, the last digit of the cube root = 2
3³	=	27	=>	If the last digit of the perfect cube = 7, the last digit of the cube root = 3
4³	=	64	=>	If the last digit of the perfect cube = 4, the last digit of the cube root = 4
5³	=	125	=>	If the last digit of the perfect cube =5, the last digit of the cube root = 5
6³	=	216	=>	If the last digit of the perfect cube = 6, the last digit of the cube root = 6
7³	=	343	=>	If the last digit of the perfect cube = 3, the last digit of the cube root = 7
8³	=	512	=>	If the last digit of the perfect cube = 2, the last digit of the cube root = 8
9³	=	729	=>	If the last digit of the perfect cube = 9, the last digit of the cube root = 9
10³	=	1000	=>	If the last digit of the perfect cube = 0, the last digit of the cube root = 0

It’s very easy to remember the relations given above because 

1	->	1	(Same numbers)
8	->	2	(10’s complement of 8 is 2 and 8+2 = 10)
7	->	3	(10’s complement of 7 is 3 and 7+3 = 10)
4	->	4	(Same numbers)
5	->	5	(Same numbers)
6	->	6	(Same numbers)
3	->	7	(10’s complement of 2 is 7 and 3+7 = 10)
2	->	8	(10’s complement of 2 is 8 and 2+8 = 10)
9	->	9	(Same numbers)
0	->	0	(Same numbers)

Also See
8 ->  2 and 2 ->  8
7 -> 3 and 3-> 7

Example 1:  Find Cube Root of 4913

Step 1:

Identify the last three digits and make groups of three three digits from right side. That is 4913 can be written as           
4,   913

Step 2 

Take the last group which is 913.  The last digit of 913 is 3.

Remember point 2, If the last digit of the perfect cube = 3, the last digit of the cube root = 7

Hence the right most digit of the cube root  = 7

Step 3

Take the next group which is 4 .

Find out which maximum cube we can subtract from 4 such that the result >= 0.
We can subtract 1³ = 1 from 4 because 4 - 1 = 3 (If we subtract 2³ = 8 from 4,   4 – 8 = -4 which is < 0)

Hence the left neighbor digit of the answer  = 1. 

That is , the answer = 17