Certainly! Let's break down and solve the expression step-by-step:
We need to evaluate [tex]\( 2 \sqrt[3]{4} + 7 \sqrt[3]{32} + \sqrt[3]{108} \)[/tex].
### Step 1: Evaluate [tex]\( 2 \sqrt[3]{4} \)[/tex]
First, we calculate [tex]\( \sqrt[3]{4} \)[/tex]:
[tex]\[ \sqrt[3]{4} \approx 1.5874010519681994 \][/tex]
Now, multiply this value by 2:
[tex]\[ 2 \times 1.5874010519681994 \approx 3.1748021039363987 \][/tex]
### Step 2: Evaluate [tex]\( 7 \sqrt[3]{32} \)[/tex]
Next, we calculate [tex]\( \sqrt[3]{32} \)[/tex]:
[tex]\[ \sqrt[3]{32} \approx 3.1748021039363987 \times 2 \approx 6.561 \][/tex]
Now, multiply this value by 7:
[tex]\[ 7 \times \sqrt[3]{32} \approx 22.22361472755479 \][/tex]
### Step 3: Evaluate [tex]\( \sqrt[3]{108} \)[/tex]
Next, we calculate [tex]\( \sqrt[3]{108} \)[/tex]:
[tex]\[ \sqrt[3]{108} \approx 4.762203155904598 \][/tex]
### Step 4: Sum all the terms
Finally, we sum [tex]\( 2 \sqrt[3]{4} \)[/tex], [tex]\( 7 \sqrt[3]{32} \)[/tex], and [tex]\( \sqrt[3]{108} \)[/tex]:
[tex]\[ 3.1748021039363987 + 22.22361472755479 + 4.762203155904598 \approx 30.160619987395787 \][/tex]
Thus, the value of [tex]\( 2 \sqrt[3]{4} + 7 \sqrt[3]{32} + \sqrt[3]{108} \)[/tex] is approximately [tex]\( 30.160619987395787 \)[/tex].
