Question

cube root of 389017 by estimated method(with steps

Answer 1

First divide the number into groups of three digits beginning from the ones' digit as follows :

389 | 017
Group II | Group II

Answer 2

Group I ends in 7. Now we have to find a digit A such that A*A*A ends in 7. With a little hit and trial we find 3*3*3 = 27 ends in 7.

Answer 3

Group II is 389. Now we find a number B such that B*B*B ≤ 389
With a little hit and trial we find 7*7*7 = 343 ≤ 389
8*8*8 = 512 which is more than 389

Answer 4

From Group I we got the digit 3 and we take it as ones' digit
From Group II we get the digit 7 and we take it as tens' digit

Now we calculate 73^3 and find it is 389017

so cube root of 389017 is 73.

Answer 5

Another way could be
389,017 < 400,000

50*50*50 = 125,000
60*60*60 = 216,000
70*70*70 = 343,000
80*80*80 = 512,000

so cube root of 389017 lies between 70 and 80

now the no 389017 ends in 7 so we find by hit and trial (as above) that 3*3*3 = 27

so we try 73^3 and find it is equal to 389017

so cube root of 389017 is 73

Answer 6

This follows Harkirat's initial logic and is documented here:
http://mbawrites.com/mba/cat/how-to-calculate-cube-roots-in-less-than-5-seconds/

I summarize the process for this case:

Memorize cubes up to nine and find the cube that is less then 389; this would be 7, since 7^3 is 343 and 8^3 is 512. So 7 is the ten's digit
Memorize the last digit of the cubes from 1 to 9, this becomes the unit portion of the answer Since the last digit is 7, the units digit is 3.

Ans. 73