Find 3 geometric means between 81 and 1
note that 81 = 3^4
so, you want
1,3,9,27,81,...
To find the geometric means between two numbers, we need to find the number that, when multiplied by itself a certain number of times, gives us the second number.
In this case, we need to find three geometric means between 81 and 1.
To find the first geometric mean, we take the square root of the product of 81 and 1:
First geometric mean = √(81 * 1) = √81 = 9
To find the second geometric mean, we take the square root of the product of 9 and 1:
Second geometric mean = √(9 * 1) = √9 = 3
To find the third geometric mean, we take the square root of the product of 3 and 1:
Third geometric mean = √(3 * 1) = √3
So, the three geometric means between 81 and 1 are 9, 3, and √3.