How many numbers between 100 to 10000 which are in the form $n^3$ ?

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Answer 1 · 2018-08-04T17:22:18

There are $17$ cubic numbers.

First find the highest cube less than $100$

$root3(100) = 4.64....$

$4^3 =64$

The first cube bigger than $10,000:$

$root3(10,000) = 21.54.......$

Therefore all the cubes from $5^3$ to $21^3$ lie between $10 and 10,000$

There are $21-4 =17$ cubic numbers

How many numbers between 100 to 10000 which are in the form n^3n^3 ?