Answer with step-by-step explanation:
Let us find the perfect cubes between 1 to 100.
We know that, 1
3
=1,2
3
=8,3
3
=27,4
3
=64 and the rest numbers i.e. 4,5,6,.... have their cubes greater than 100.
So, only these four numbers have their cubes between 1 to 100.
Thus, there are 4 perfect cubes from 1 to 100.
Now, let's find the cubes between −100 to 0
We know, 0
3
=0,(−1)
3
=−1,(−2)
3
=−8,(−3)
3
=−27,(−4)
3
=−64 and the rest numbers have their cubes less than −100
So, only these 5 numbers have their cubes between −100 to 0 and 4 perfect cubes are there from 1 to 100.
Thus, there are 9 perfect cubes from −100 to 100.
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