Answer
Pythagorean Theorem is verified.
Work Step by Step
Given the vectors ${u}=(3,-2), \quad {v}=(4,6)$, then their lengths can be calculated as follows
$$\|{u}\|^2=9+4=13, \quad \|{v}\|^2=16+36=52.$$
Since $u+v=(7,4)$, then
$$\|{u+v}\|^2=49+16=65.$$
One can see that,
$$\|{u}+{v}\|^{2}=\|{u}\|^{2}+\|{v}\|^{2}$$
Hence, Pythagorean Theorem is verified.