Estimating Cube Root, this method will work only if the given number is a perfect cube. The following are the steps to estimate the cube root.
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 = 36).
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 238328.
Solution :
238328 is an even number so its cube root has to an even number. Make two groups ---> 238328
First group 328 ---> unit digit is 8 so unit digit of cube root will be 2. (see the above table).
Second Group 238 -----> it lies between 6^{3}=216 and 7^{3} =343 .
So take the smaller number 6 as ten's place.
∴ ∛238328 = 62
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2) Find the cube root of -175616.
Solution :
We know that ∛-175616 = - ∛175616
The number is even so its cube root has to an even number.
Make two groups ---> 175616
First group 616 ---> unit digit is 6 so unit digit of cube root will be 6 (see the above table).
Second Group 175 -----> it lies between 5^{3}=125 and 6^{3} = 216 .