You are given the numbers {32 + n, n
/8,√n+225 }. Find the

smallest value of n so that all of the numbers in the set are natural numbers

Respuesta :

{32 + n , n/8 , √n + 225 }.
The smallest natural number should abide by 2 conditions:

1st: n/8 = Natural number (integer)  and
2nd: 
√n = also it should be integer

n should be a multiple of 8 (8,16,24,32,40,48,56,64..)
Among all the multiples, only 64 is a perfect square, then n =64,
Proof:
32 + n = 32+64 = 96 =Natural number
n/8 = 64/8 = 8 = Natural number
√n + 225 = √64 + 225 = 8 + 225 = 233 =  Natural number