Question

How can we find the cube root of a 7 , 8 or 9 digit number like 1906624 using estimation method?

Answer 1

Estimation method :

Step I : Make groups of 3 digits from unit(one's) place.This the 1st group.The remaining number makes the 2nd group.

Step II : The unit's digit of the 1st group will decide the unit digit of the cube root.( if the unit digit of the cube is 6 then the unit digit of cube root will also 6 as 6 x 6 x 6 = 3 6 ).

Step III : Find the cube of numbers between which the 2nd group lie.

Step IV : Take the smaller number as its ten's digit.

Unit digit of a given number	Unit digit of cube root
1	1
3	7
4	4
5	5
6	6
7	3
8	2

Examples on estimating cube root :

1) Find the cube root of 1906624.

Solution :
1906624 is an odd number so its cube root has to an odd number.
Make three groups ---> 1, 906,624

First group 624 ---> unit digit is 4 so unit digit of cube root will be 4.
(as per the above table).

Second Group 1906 -----> it lies between 12 ³ = 1331 and 13³ =2197

So take the smaller number 12 as ten's place.


∴ ∛1906624 = 124 Ans.