Conocemos los productos: a·b =8; a·c = 10; b·c = 15¿Cómo hallamos el producto a·b·c conuna aproximación de dos decimalessin 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:

• $a \cdot b = 8$
• $a \cdot c = 10$
• $b \cdot c = 15$

2. Relevant Concepts

We can use the relation between these products to calculate $(a \cdot b \cdot c)^2$: $(a \cdot b \cdot c)^2 = (a \cdot b) \cdot (a \cdot c) \cdot (b \cdot c)$

3. Analysis and Detail

Using the given products to find $(a \cdot b \cdot c)^2$: $(a \cdot b \cdot c)^2 = (8) \cdot (10) \cdot (15)$ Calculating this step-by-step:

1. First calculate $8 \cdot 10 = 80$
2. Next, calculate $80 \cdot 15 = 1200$

Thus, $(a \cdot b \cdot c)^2 = 1200$

To find $a \cdot b \cdot c$: $a \cdot b \cdot c = \sqrt{1200}$

Calculating $\sqrt{1200}$: $\sqrt{1200} = \sqrt{100 \cdot 12} = 10 \cdot \sqrt{12} = 10 \cdot 2\sqrt{3} \approx 10 \cdot 3.4641 \approx 34.6414$ So, rounding it to two decimals: $a \cdot b \cdot c \approx 34.64$

4. Verify and Summarize

We verified the calculations step-by-step. The calculation for $(a \cdot b \cdot c)^2$ holds true.

Final Answer

The product $a \cdot b \cdot c$ is approximately $34.64$.