How to find cube root of 8 or 9 digit number

Before going to find out cube of a long digit number we go through the short 3 digit number.

Cube Roots up to 3 Digits

If you had to calculate the cube root of a 3 digit number, it would be quite easy. Here is a table of cubes from 1 to 10:

n	n3
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000

To do cube roots of 9 digit numbers, you are going to have to be familiar with these first 10 cubes. So you might as well memorise them. And if you have memorised them, then there isn’t really any trick to calculating the cube roots.

Cube Roots up to 6 Digits

Let see the table below:

NUMBER	CUBE	LAST DIGIT OF CUBE
0	0	0
1	1	1
2	8	8
3	27	7
4	64	4
5	125	5
6	216	6
7	343	3
8	512	2
9	729	9

 

We will follow these steps to find the cube root of a number:

1. Ignore the last 3 digits of the number. Let remaining number be “I”.


2. From the above table check which number’s cube is less than or equal to ‘I’. It will be left part of our answer. Let it be “L”.


3. Let Right part of our answer be “R”. It will be determined from the above table. For Ex. If last digit of question is 7, then last digit of our answer will be 3.


4. Our answer will be L|R.

Example 1

Suppose we want to find the cube root of 21952.

Step 1: Ignore last three digits of 21952. Remaining number left is ’21′.

Step 2: From the above table cube of ’2′ is less than ’21′. Therefore left part (L) of our answerwill be ’2′.

Step 3: Since last digit of  ‘21952‘ is ‘2‘. Therefore right part (R) of our answer will be ’8′. (Because Last digit of ‘cube of 8′ is 2. see table above.)

Step 4: Our Answer will be L|R. Therefore Answer will be 2|8 = 28.

Example 2

Suppose we want to find the cube root of 636056.

Step 1: Ignore last three digits of 636056. Remaining number left is ’636′.

Step 2: From the above table cube of ’8′ is less than ’636′. Therefore left part (L) of our answerwill be ’8′.

Step 3: Since last digit of  ‘636056‘ is ‘6‘. Therefore right part (R) of our answer will be ’6′. (Because Last digit of ‘cube of 6′ is 6. see table above.)

Step 4: Our Answer will be L|R. Therefore Answer will be 8|6 = 86.

Cube Roots up to 8 or 9 Digits

we can easily calculate the first digit by considering the 1st 2(two) digit (if given number 8 digit) or 1st 3 digit (if given number 9 digit)  and last digits of the number by previous technique of a 8 digit or 9 digit number .

So, for example, looking at 580093704, we compare . The first 3 digit is 580 which is greater than 512(8^3).So first digit is 8., and the last digit of the cube root must be 4 as you have learned before.

So the next question is about middle digit.

To find out the middle digit we need a different module,11 module.

There is a short cut for modulo 11, but it is a little harder. Starting from the right end, you alternatively add and subtract digits. So if the number is 580093704. 580093704 = 4 – 0 + 7 – 3 + 9 – 0 + 0 – 8 + 5 = 14 = 4 – 1 = 3 (modulo 11). (In this case we luckily ended up with a positive number less than 11, but you might have to adjust the answer to a number in this range by adding or subtracting 11.)

To make use of these moduli, we need to calculate the table of cubes mod  11:

n	n3	n3 mod 11
0	0	0
1	1	1
2	8	8
3	27	5
4	64	9
5	125	4
6	216	7
7	343	2
8	512	6
9	729	3
10	1000	10

we can see that each value from 0 to 10 occurs only once in the list of cubes modulo 11 (from 0 to 10), which means that cube roots can be calculated modulo 11.

Returning back to the worked example, 580093704 = 3 modulo 11, so (looking at the table, which, by the way, you will have to memorize) its cube root = 9 modulo 11. We’ve already determined that the first digit is 8 and the last digit is 4. If we think of the cube root as 8x4, for some x, then we have the equation 4 -x + 8 = 9 modulo 11, i.e. 12 - x = 9 modulo 11, so x = 3 modulo 11. Which gives a final (and correct) answer of 834.

Example 1(8 digit):

Take a number 16777216

Step 1: Take first two(2) digit of the number i.e. 16 which is greater than 8(2^3) and less than 27(3^3)

so first digit is 2.

Step 2:Last digit of the given number is 6.So last digit is 6.

Step 3:let the number is 2×6 where ‘x’ is unknown.

Apply 11 module:6-1+2-7+7-7+6-1=5 of module

5 of module means 3 from table above.

so 6-x+2=3

gives x=5

So the cube root 16777216 is 256

So that,s all to find out cube root of 8 or 9 digit number.

Hope this will help you to guide.

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How to find cube root of 8 or 9 digit number