Answered

Get detailed and reliable answers to your questions on IDNLearn.com. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

Simplify the expression:
[tex]\[ 2 \sqrt[3]{4} + 7 \sqrt[3]{32} + \sqrt[3]{108} \][/tex]

Sagot :

GinnyAnsweridn
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].
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.