Sure! Let’s solve the expression step by step:
[tex]\[
\sqrt[3]{3^2 \times 5^2} \times 2 \sqrt[3]{3 \times 5}
\][/tex]
First, we’ll break down the expression into two separate cube roots:
1. Evaluate [tex]\(\sqrt[3]{3^2 \times 5^2}\)[/tex]
2. Evaluate [tex]\(\sqrt[3]{3 \times 5}\)[/tex]
3. Multiply the results together and then multiply by 2.
### Step 1: Evaluate [tex]\(\sqrt[3]{3^2 \times 5^2}\)[/tex]
First, calculate [tex]\(3^2 \times 5^2\)[/tex]:
[tex]\[
3^2 = 9 \quad \text{and} \quad 5^2 = 25
\][/tex]
[tex]\[
3^2 \times 5^2 = 9 \times 25 = 225
\][/tex]
Now take the cube root of 225:
[tex]\[
\sqrt[3]{225} \approx 6.0822 \quad \text{(approximately 6.082201995573399)}
\][/tex]
### Step 2: Evaluate [tex]\(\sqrt[3]{3 \times 5}\)[/tex]
First, calculate [tex]\(3 \times 5\)[/tex]:
[tex]\[
3 \times 5 = 15
\][/tex]
Now take the cube root of 15:
[tex]\[
\sqrt[3]{15} \approx 2.4662 \quad \text{(approximately 2.46621207433047)}
\][/tex]
### Step 3: Multiply the results and then multiply by 2
Now, multiply the results from Step 1 and Step 2 together:
[tex]\[
6.0822 \times 2.4662 \approx 14.999999999999996 \quad \text{(approximately 14.999999999999993)}
\][/tex]
Finally, multiply by 2:
[tex]\[
2 \times 14.999999999999996 \approx 30 \quad \text{(approximately 29.999999999999993)}
\][/tex]
So, the value of [tex]\(\sqrt[3]{3^2 \times 5^2} \times 2 \sqrt[3]{3 \times 5}\)[/tex] is approximately 30.
