Question 76

How many numbers are there from 2000 to 7000 which are both perfect squares and perfect cubes?

Solution

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)

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: