Sunday, October 28, 2018

Cube Roots of Perfect Cubes

Calculate cube roots of perfect cubes in seconds.

Preparation:

1. Memorize the cubes of 1 to 10 shown 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, remember the following properties.

If the last digit of the perfect cube = 1, 4, 5, 6, 9 & 0, the last digit of cube root is equal to that number.
If the last digit of the perfect cube = 2, 3, 7 & 8, the last digit of the cube root = 8, 7, 3 & 2 respectively, their  10’s complement.

It’s very easy to remember.
1  ->  1  (Same numbers)
8  ->  2 (8+2 = 10)
7  ->  3 (7+3 = 10)
4  ->  4 (Same numbers)
5  ->  5 (Same numbers)
6  ->  6 (Same numbers)
3  ->   7 (3+7 = 10)
2  ->   8  (2+8 = 10)
9  ->   9 (Same numbers)
0  ->   0 (Same numbers)
Take note also that
8 -> 2 and 2 ->  8 
7 -> 3 and 3-> 7

Example 1:  Find Cube Root of 4913

Step 1
Split the digits, group of 3 digits.
      4        913

Step 2
Take the first group which is 4 .
Find out a maximum cube that is not greater than 4. Use 1³ = 1.
Hence the first digit of the answer  = 1

Step 3
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 last digit of the cube root  = 7

That is, the answer = 17

More examples:

Cube root of 804357 ?       
804           357
9³ = 729          7
9                     3
Answer: 93

Cube root of 9261 ?
9              261
2³ = 8              1
2                     1
Answer: 21

Cube root of  32768 ?
32               768
3³ = 27            8
3                     2
Answer: 32

Cube root of 97336 ?
97            336
4³ = 64            6
4                     6
Answer: 46

Cube root of 216000 ?
216          000
6³ = 216          0
6                     0
Answer: 60

It is as simple as that, all you need to do is memorize the cubes of 1 to 10.

#Matamata

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