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.

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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