If x^2 + y^2 + z^2 = 125 and xy + yz + za = 250, then $x$ + $y$ + z is ________.

Step 1 (Recall multi-variable algebraic identity): The square of a trinomial is given by:

Step 2 (Substitute the values): We substitute the given values $x^2+y^2+z^2=125$ and $xy+yz+za=250$:

Step 3 (Solve for x + y + z): Taking the square root of both sides:

(Note: Assuming the sum is positive as is standard in high-school contest algebra).

Step 4 (Conclusion): The value of $x+y+z$ is exactly 25.