Question

you are given numbers, {30 + n, n/3, square root n+16}. Find the smallest value of n so that all of the numbers in the set are natural numbers.

Answer 1

Answer:   n = 9

========================================================

Explanation:

Let's assume that n is not negative. If we tried the smallest nonnegative value, n = 0, then we get

• 30+n = 30+0 = 30
• n/3 = 0/3 = 0
• sqrt(n+16) = sqrt(0+16) = 4

The middle result 0 isn't a natural number. The set of natural numbers is {1,2,3,4,...} which is the set of positive whole numbers.

So we can't use n = 0.

Through trial and error, you should find that n = 9 is the next value we can try such that sqrt(n+16) is a natural number, and so is n/3.

If n = 9, then,

• 30+n = 30+9 = 39
• n/3 = 9/3 = 3
• sqrt(n+16) = sqrt(9+16) = 5

We see that the middle result is now larger than 0 and it's a natural number. The same can be said for the last result as well.