=(√a) square +(√b) square -2 √ a √ b

=(√a-√b) squared

≥0

∴ ? a+b≥2√(ab)

∴ ? (a+b)/2≥√(ab)

Pay attention to the significance of geometric average is:

The area of a square is equal to the area of a rectangle whose length and width are a and b respectively.

The side length of this square is the geometric average of a and B.