How do you evaluate vector magnitudes which include multiplication?

Question

For the vectors u= (1,3,0) and v=(3,0,2), how do I find the magnitude of u+4v? For letters u and v, I try adding all 3 components of the vectors, squaring each component, then square rooting it. For v, I multiple everything by 4. Then, I had the results together. Yet, this is incorrect. What is the proper way to evaluate this? A picture is attached so that the original problem may be referenced. Also, please feel free to edit my post as needed for clarity. I am still trying to figure out the layout of this site. enter image description here

Answer 1

The norm (or magnitude) of $(a,b,c)$ is $\sqrt {a^{2}+b^{2}+c^{2}}$. First square the components, then add them and take the square root at the end. Ex: $u+4v=(13,3,8)$ and its magnitude) is $\sqrt {169+9+64}=\sqrt {242}$.

Answer 2

$$|u+4v|=|(1,3,0)+4(3,0,2)|=|(13,3,8)|=...$$ I got $11\sqrt2.$