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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