Conocemos los productos: a·b = 8; a·c = 10; b·c = 15¿Cómo hallamos el producto a·b·c con una aproximación de dos decimales sin conocer los valores de a, b y c?

1. Break Down the Problem

We need to find the product $a \cdot b \cdot c$ using the given products $a \cdot b = 8$, $a \cdot c = 10$, and $b \cdot c = 15$.

2. Relevant Concepts

To find $a \cdot b \cdot c$, we can use the following relationship: $(a \cdot b)(a \cdot c)(b \cdot c) = (a \cdot b \cdot c)^2$

3. Analysis and Detail

1. Using the products given, we can substitute: $(a \cdot b) = 8, \quad (a \cdot c) = 10, \quad (b \cdot c) = 15$
2. Now, compute the left-hand side: $(8)(10)(15) = 1200$
3. Set this equal to $(a \cdot b \cdot c)^2$: $(a \cdot b \cdot c)^2 = 1200$

4. Verify and Summarize

Now, we take the square root to find $a \cdot b \cdot c$: $a \cdot b \cdot c = \sqrt{1200}$ Calculating the square root: $\sqrt{1200} = \sqrt{100 \cdot 12} = 10 \sqrt{12} \approx 10 \cdot 3.464 = 34.64 \quad (\text{approximately})$

Final Answer

Thus, the product $a \cdot b \cdot c$ is approximately $34.64$.