Question

find the cube root of 8000 through estimation

Answer 1

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 ---> 238 328
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

And your answer is....

20....

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Answer 2

given number is 8000

unit digit is 0

=Unit digit of the cube root of the given number is 0

number obtained after striking out three digit from the extreme right ( units,tens and hundreds digits )=800