Question

how many numbers between 1 and 2000 inclusive have both square root and cube root as integer

Answer 1

There are 3 numbers in this range:

 

1, 64, and7291, 64, and729

 

The following one with this prerequisite met is 163=2(4×3) =4096163=2(4×3)=4096

 

For this announcement to be valid in any case, the number being cubed must be a "square number" - a number that has been increased without anyone else's input to get this number. For this situation, we have 6 numbers that were in this range:

 

±1, ±2, and±3±1, ±2, and±3