Alright, let's solve the expression [tex]\(\sqrt[3]{16} + 3 \sqrt[3]{54}\)[/tex] step by step.
### Step 1: Calculate the cube root of 16
First, we need to determine [tex]\(\sqrt[3]{16}\)[/tex].
After calculating, we find:
[tex]\[
\sqrt[3]{16} \approx 2.5198420997897464
\][/tex]
### Step 2: Calculate the cube root of 54
Next, we need to determine [tex]\(\sqrt[3]{54}\)[/tex].
After calculating, we find:
[tex]\[
\sqrt[3]{54} \approx 3.7797631496846193
\][/tex]
### Step 3: Multiply the cube root of 54 by 3
Now, we multiply the result from Step 2 by 3:
[tex]\[
3 \times \sqrt[3]{54} \approx 3 \times 3.7797631496846193 = 11.339289449053858
\][/tex]
### Step 4: Sum the results
Finally, we add the results from Step 1 and Step 3 together:
[tex]\[
\sqrt[3]{16} + 3 \sqrt[3]{54} \approx 2.5198420997897464 + 11.339289449053858 = 13.859131548843605
\][/tex]
### Conclusion
Thus, the value of the expression [tex]\(\sqrt[3]{16} + 3 \sqrt[3]{54}\)[/tex] is approximately:
[tex]\[
13.859131548843605
\][/tex]
To summarize:
- [tex]\(\sqrt[3]{16} \approx 2.5198420997897464\)[/tex]
- [tex]\(\sqrt[3]{54} \approx 3.7797631496846193\)[/tex]
- [tex]\(3 \times \sqrt[3]{54} \approx 11.339289449053858\)[/tex]
- The total sum is [tex]\(\approx 13.859131548843605\)[/tex]
