How many numbers are there from 2000 to 7000 which are both perfect squares and perfect cubes?
Numbers which are both perfect squares and perfect cubes are of the form = $$k^6$$, where $$k$$ is a natural number.
Thus, numbers are = $$(1)^6$$ , $$(2)^6$$ , $$(3)^6$$ , $$(4)^6$$ , $$(5)^6$$
= 1 , 64 , 729 , 4096 , 15625 , and so on
From the list of above numbers, we can see that only 1 number i.e. 4096 lies between 2000 and 7000
=> Ans - (B)
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