how to find geometric mean of 1÷3and 64 ÷3 find geometric mean

To find the geometric mean of two numbers, you multiply them together and then take the square root of the product.

Given numbers: \(\frac{1}{3}\) and \(\frac{64}{3}\)

1. **Multiply the numbers:**
   \[
   \frac{1}{3} \times \frac{64}{3} = \frac{1 \times 64}{3 \times 3} = \frac{64}{9}
   \]

2. **Take the square root of the product:**
   \[
   \text{Geometric Mean} = \sqrt{\frac{64}{9}} = \frac{\sqrt{64}}{\sqrt{9}} = \frac{8}{3}
   \]

So, the geometric mean of \(\frac{1}{3}\) and \(\frac{64}{3}\) is \(\frac{8}{3}\).

Would you like more details or have any questions?

Here are some related questions:

1. How do you find the geometric mean of more than two numbers?
2. What is the difference between arithmetic and geometric means?
3. How do you calculate the geometric mean for negative numbers?
4. Can the geometric mean be used for sets of data that include zero?
5. What is the geometric mean used for in real-life applications?

**Tip:** The geometric mean is often used to calculate average rates of growth over time, especially when dealing with percentages or ratios.

Learn how to calculate the geometric mean of two fractions, 1/3 and 64/3, using multiplication and square root operations. Understand the concept of geometric mean and its application in mathematics.

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