# Thread: Of Squares & Cubes

1. ## Of Squares & Cubes

The question is...

The number of integers between 1 & 1000(both inclusive) which are neither perfect squares nor perfect cubes is?

I sarted off like this-
(tried to count the number of digits which are perfect squares & cubes)

1-1-1
2-4-8
3-9-27
4-16-64
5-25-125
6-36-216
7-49-343
8-64-512
9-81-729
10-100-1000
11-121
12-144
.......
which goes upto 31 squared as 32 square > 1000

on counting all the red ones i get 40,

so the answer i got was 960 (which is two less than the given answer)

The question is...

The number of integers between 1 & 1000(both inclusive) which are neither perfect squares nor perfect cubes is?

I sarted off like this-
(tried to count the number of digits which are perfect squares & cubes)

1-1-1
2-4-8
3-9-27
4-16-64
5-25-125
6-36-216
7-49-343
8-64-512
9-81-729
10-100-1000
11-121
12-144
.......
which goes upto 31 squared as 32 square > 1000

on counting all the red ones i get 40,

so the answer i got was 960 (which is two less than the given answer)

You have double counted two elements one of them is

$64=8^2=4^3$

I don't know the other of the top of my head

3. Originally Posted by TheEmptySet
You have double counted two elements one of them is

$64=8^2=4^3$

I don't know the other of the top of my head
yes another one to go.............

The other is $729=27^2=9^3$
The other is $729=27^2=9^3$