Cube Roots of Perfect Cubes Using Vedic Mathematics

Cube Roots of Perfect Cubes Using Vedic Mathematics
➖➖➖➖➖➖➖
 Points to remember
✔ To calculate cube root of any perfect cube quickly, we need to remember the cubes of 1 to 10 and we need to remember an interesting property.


⏺1³ = 1
If last digit of perfect cube =1,
last digit of cube root =1


⏺2³ = 8
If last digit of perfect cube =2,
last digit of cube root =8

⏺3³ = 27
If last digit of perfect cube =3,
last digit of cube root =7

⏺4³ = 64
If last digit of perfect cube =4,
last digit of cube root =4

⏺5³ = 125
If last digit of perfect cube =5,
last digit of cube root =5

⏺6³ = 216
If last digit of perfect cube =6,
last digit of cube root =6

⏺7³ = 343
If last digit of perfect cube =7,
last digit of cube root =3

⏺8³ = 512
If last digit of perfect cube =8,
last digit of cube root =2

⏺9³ = 729
If last digit of perfect cube =9,
last digit of cube root =9

⏺10³ = 1000
If last digit of perfect cube =0,
last digit of cube root =0
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
✔ It’s very easy to remember the relations given above as follows.

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 3 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
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
✔ Now let’s see how we can actually find out cube roots of perfect cubes faster.

Eg. : Find Cube Root of 4913
 Step 1➡ Identify the last three digits and make groups of three three digits from right side. i.e. 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 last digit of perfect cube=3, last digit of 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
i.e., answer =17✅


Eg: Find Cube Root of 804357
 Step 1 ➡ Identify the last three digits and make groups of three three digits from right side. i.e., 804357 can be written as
✅804, 357

 Step 2 ➡ Take the last group which is 357. The last digit of 357 is 7.
Remember point 2, If last digit of perfect cube =7 , last digit of cube root =3
✅Hence the right most digit of the cube root =3

 Step 3 ➡ Take the next group which is 804
Find out which maximum cube we can subtract from 804 such that the result ≥ 0
We can subtract 9³=729 from 804 because 804−729=75 (If we subtract 10³=1000 from 729, 729–1000=−271 which is <0)

Hence the left neighbor digit of the answer =9
i.e., answer =93.✅