The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

Let the numbers be a, b and c.

Then, a² + b² + c² = 138 and (ab + bc + ca) = 131.

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) = 138 + 2 x 131 = 400.

 (a + b + c) = √400 = 20.