Question

What is the geometric mean of 1, 2, 8, and 16? 05 7 06 04

Answer 1

The geometric mean of 1, 2, 8, and 16 is calculated by multiplying the numbers and taking the fourth root of the product, resulting in a geometric mean of 4.

Step-by-step explanation:

The geometric mean of a set of numbers is the nth root of the product of the numbers, where 'n' is the number of terms. In the case of the numbers 1, 2, 8, and 16, the calculation of the geometric mean involves multiplying these numbers together and then taking the fourth root, since there are four numbers in this set.

To calculate the geometric mean:

1. Multiply the numbers together: 1 \(\times\) 2 \(\times\) 8 \(\times\) 16 = 256.
2. Since we have 4 numbers, we take the fourth root of 256, which is \(\sqrt[4]{256}\).
3. The fourth root of 256 is 4, since \(4 \times 4 \times 4 \times 4 = 256\).

Therefore, the geometric mean of 1, 2, 8, and 16 is 4.

Answer 2

The geometric mean of 1, 2, 8, and 16 is calculated by multiplying the numbers together and taking the fourth root of the product, which results in a geometric mean of 4.

Step-by-step explanation:

The geometric mean is a type of mean or average, which indicates the central tendency of a set of numbers by using the product of their values. To calculate the geometric mean of 1, 2, 8, and 16, you would multiply the numbers together and then take the nth root, where n is the number of terms. In this case, n is 4 since there are four numbers.

The calculation would be as follows: (1 \times 2 \times 8 \times 16)^(1/4). This equals 2,048^(1/4), which when calculated gives the geometric mean of 4.

This method is useful when dealing with products of different factors and represents the typical value of a set of numbers in multiplicative terms.