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The number of natural numbers less that or eual to 2985984 which are neither perfect squares nor perfect cubes are: a) 2984124 b) 2984244 c) 2959595 d) none. please explain to me how to solve this problem.

The number of natural numbers less that or eual to 2985984 which are neither perfect squares nor perfect cubes are:


a) 2984124 b) 2984244 c) 2959595 d) none.


please explain to me how to solve this problem.

Grade:

1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

√2985984=1728
3√2985984=144

so the number of perfect squares less than equal to 2985984 = 1728
so the number of perfect cubes less than equal to 2985984 = 144

Number of numbers which are both cubes and perfect squares=12


Numbers which are perfect squares or cubes=1728+144-12=1716+144=1860

hence the numbers which are neither squares nor cubes is
2985984-1860=2984124.

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Sagar Singh

B.Tech, IIT Delhi

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