Answer:
n = 9
Step-by-step explanation:
We require to consider [tex]\sqrt{n+16}[/tex]
For it to be a natural number then it must be a perfect square
If n = 9 , then
[tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5
and
[tex]\frac{n}{3}[/tex] = [tex]\frac{9}{3}[/tex] = 3
34 + n = 34 + 9 = 43
5, 3, 43 ∈ natural numbers
Then n = 9 is the smallest value
