How do you find the smallest positive integer of a variable in a cube root so that the cube root is an integer ex. find the smallest positive integer g so that the cube root of 400g is an integer?

Answer 1

Here is a method:

cube root of 400g = n, where n is an integer

cube both sides: 400g = n3

then: g = n3/400

therefore: n3/400 must be an integer

if this is so, then n3 must be divisible by 400 with no remainder,

and n must be => cube root of 400 which is 7.368

bracket the answer by substitution:

let n=8, n cubed = 512 no good

let n=12, n cubed = 1728 no good

let n=20, n cubed = 8000, 8000/400=20 OK

No smaller value of n will be divisible by 400 without a remainder, so g=20 is the smallest positive integer that meets the requirement.