Given 9 and 16, try to write a number a so that one of the three numbers is the square root of the product of the other two numbers. How many numbers can you write

Given 9 and 16, try to write a number a so that one of the three numbers is the square root of the product of the other two numbers. How many numbers can you write

There are only three possibilities. Suppose the third number is a
1、A*A=9*16
2、16*16=9*A
3、9*9= 16*A
So the possible numbers are 12; 256 / 9; 81 / 16