How do I solve this math question?

Question

What is the farthest away that two points in space can be, if the first is on the surface of the sphere with center (1, -4, 9) and radius 15 and the other on the surface of the sphere with center (-3, 10, -6) and radius 17^1/2

Answer 1

First, find the distance between the centers. Taking the differences in 3 axes, we get:

X: 1 - (-3) = 5

Y: -4 - 10 = -14

Z: 9 - (-6) = 15

The distance between the centers is then the square root of the sum of the squares:

√(5² + 14^{2 +} 15²) = √446

The maximum distance is then √446 + 15 + √17