Answer:
208 should be multiplied by 13 to make it a perfect square.
The product will be 2704 and its square root is 52.
Explanation:
I used excel to solve this.
In column A, I put numbers from 1 to 60.
In column B, I put the square of column A (these are our perfect squares).
In columns C I put column B divided by 208.
Then I looked for the first spot where column C produced an integer. It was on row 52.