Q&A for How to Calculate the Geometric Mean

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To make this trivially easy, use logarithms Base 2. Then the logarithms are 1, 2, 4, and 5. The simple average of those logarithms is 3, so the geometric mean of 2, 4, 16, and 32 is 2^3 = 8.

3 x 7 = 21. √21 = 4.58.

To find the geometric mean of two numbers, just find the product of those numbers and take the square root.

First you need to find the product of your two numbers. In this case 12 multiplied by 96 = 1152. Then you want to find the nth root of the product (as there are only two numbers, the nth root is the square root of the product). Hence you square root 1152 and this produces the geometric mean of 12 and 96, which is 33.9 (3s.f.)

Set it up as: (x-3)/(x+4) = (x+4)/(2x+8). That simplifies to: x + 4 = 2x - 6, which quickly yields x = 10.

Do it the same way you do it with whole numbers.

No, there must be at least two numbers.

Multiply 81 by 100, then find the square root of the product. Here 81 x 100 = 8,100. The square root of 8,100 is 90.

The geometric mean concept is not applicable to calendar dates.

A geometric mean is a "geometric average," situated between a smaller number and a larger number such that the smaller number can be multiplied by a given number to attain the geometric mean, and the geometric mean can be multiplied by that same given number to attain the larger number. The geometric mean is the square root of the product of the smaller and larger numbers.

Because zero is one of the numbers, and because you would multiply the other numbers by zero, the geometric mean is automatically zero.

Multiply those four numbers together to get 4,096. Find the fourth root of 4,096. The fourth root is the square root of the square root, so use a calculator to find to find the square root twice. That gives you 8.

(6)(3)(2) = 36. Then find the cube root of 36, because there are three numbers in the data set. The cube root of 36 is approximately 3.3.

(1)(3)(1)(5)(2) = 30. Because there are five numbers, take the fifth root of 30 to get the answer, which is 1.974.

(3)(108) = 324. The geometric mean is the square root of 324, which is18.

(3)(8) = 24. √24 = √[(4)(6)] = 2√6. That's the best (most accurate) answer, but you can further evaluate it to (2)(2.45) = 4.9.

You'll need a scientific calculator or a program that can find the nth root of a number. In this case you would multiply these numbers together and then find the tenth root of the product (because there are ten data points).

Multiply those six numbers together. Then use a scientific calculator or a computer program to find the sixth root of the product.

That means the square root of ax = 12, so ax = 144. Then x = 144 / a. (You can't find a numeric value for x, because you've been given a single equation in two variables.)

3√3000 = 3√[(30)(100)] = (3)(10)√30 = 30√30. You can leave the answer in that form, or you can further evaluate it: (30)(5.477) = 164.31.

There is no shortcut method. Use a scientific calculator to multiply the numbers together and then take the eighth root of that product (since there are eight numbers in the set.)