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

{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