Geometric mean of 4 and 9.
Understand the Problem
The question is asking to find the geometric mean of the numbers 4 and 9, which is computed using the formula for geometric mean, given by the square root of the product of the two numbers.
Answer
$6$
Answer for screen readers
The geometric mean of 4 and 9 is $6$.
Steps to Solve
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Identify the Numbers We start with the numbers given in the problem: 4 and 9.
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Calculate the Product Next, we find the product of the two numbers. We calculate: $$ 4 \times 9 = 36 $$
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Calculate the Square Root Now, we need to find the square root of the product we calculated in the previous step. So we will compute: $$ \sqrt{36} = 6 $$
The geometric mean of 4 and 9 is $6$.
More Information
The geometric mean is particularly useful for sets of numbers that exhibit exponential growth or are defined multiplicatively, such as in finance for calculating average rates of return.
Tips
- A common mistake is to confuse the geometric mean with the arithmetic mean. Remember, the geometric mean involves multiplication and taking the square root, while the arithmetic mean involves addition and division.
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