find a geometric means between 4096 and 972? my answers is (0.75)^4 if it wrong can you give the right answer and show the work as simple as you can. thank you
we want the square root of their product
sqrt (4096 * 972)
I do not like those big numbers so let's look for a common factor like maybe 4
yes, 4 works
sqrt [(1024*4)* (243*4) ]
= 4 sqrt (1024*243)
hmm, try 4 again
1024/4 = 256
so take 2 out
= 8 sqrt (256*243)
well we could probably divide 256 by 16 and take another 4 out but this is easy enough now
= 1995
thank you
To find the geometric mean between two numbers, you can follow these steps:
Step 1: Multiply the two numbers together. In this case, multiply 4096 and 972.
4096 * 972 = 3,982,592
Step 2: Take the square root of the result obtained in step 1.
√3,982,592 ≈ 1,997.917
Therefore, the geometric mean between 4096 and 972 is approximately 1,997.917.
Now, let me explain why your answer (0.75)^4 is incorrect:
Your answer seems to be trying to find the geometric mean through exponentiation with base 0.75. However, exponentiation is not the correct approach to finding geometric means between two numbers.
Instead, you need to use the formula of multiplying the two numbers together and then taking the square root of the result.
Remember, the correct answer is approximately 1,997.917.