Let's tackle this problem step-by-step to ensure we understand each part and the calculations involved.
### Step 1: Calculate the Cube Root of 24
First, we need to find the cube root of 24. The cube root of 24 is approximately:
[tex]\[
\sqrt[3]{24} \approx 2.8845
\][/tex]
### Step 2: Calculate the Cube Root of 45
Next, we calculate the cube root of 45. The cube root of 45 is approximately:
[tex]\[
\sqrt[3]{45} \approx 3.5569
\][/tex]
### Step 3: Calculate the Product of the Cube Roots of 24 and 45
We need to find the product of these two cube roots:
[tex]\[
\sqrt[3]{24} \cdot \sqrt[3]{45} \approx 2.8845 \times 3.5569 \approx 10.2599
\][/tex]
### Step 4: Calculate the Cube Root of 69
For this step, we calculate the cube root of 69, which is approximately:
[tex]\[
\sqrt[3]{69} \approx 4.1016
\][/tex]
### Summary of Results
- [tex]\(\sqrt[3]{24} \approx 2.8845\)[/tex]
- [tex]\(\sqrt[3]{45} \approx 3.5569\)[/tex]
- [tex]\(\sqrt[3]{24} \cdot \sqrt[3]{45} \approx 10.2599\)[/tex]
- [tex]\(\sqrt[3]{69} \approx 4.1016\)[/tex]
So, the results of the calculations are:
1. The cube root of 24 is approximately 2.8845.
2. The cube root of 45 is approximately 3.5569.
3. Their product is approximately 10.2599.
4. The cube root of 69 is approximately 4.1016.
