some means

the arithmetic mean of two numbers is

and the geometric mean of two numbers is
 

find the arithmetical mean and geometrical mean for:

a = 2, b = 18
a = 3, b = 27
a = 1, b = 81
a = 4, b = 16
a = 2, b = 50
a = 5, b = 20

• when is the arithmetical mean closest to the geometric mean?
• how close can they be?
• which one is larger?
• does this happen for larger sets of numbers?
• for just two numbers: prove, by squaring, that the arithmetical mean is larger than or equal to the geometric mean