To simplify the expression [tex]\(3 \sqrt[3]{250} + 7 \sqrt[3]{16} - 4 \sqrt[3]{54}\)[/tex], we need to evaluate each term individually and then combine the results.
1. Evaluate [tex]\(3 \sqrt[3]{250}\)[/tex]:
- Start by finding the cube root of 250.
[tex]\[
\sqrt[3]{250} \approx 6.2996
\][/tex]
- Then multiply this result by 3:
[tex]\[
3 \times 6.2996 \approx 18.8988
\][/tex]
2. Evaluate [tex]\(7 \sqrt[3]{16}\)[/tex]:
- Start by finding the cube root of 16.
[tex]\[
\sqrt[3]{16} \approx 2.5198
\][/tex]
- Then multiply this result by 7:
[tex]\[
7 \times 2.5198 \approx 17.6389
\][/tex]
3. Evaluate [tex]\(4 \sqrt[3]{54}\)[/tex]:
- Start by finding the cube root of 54.
[tex]\[
\sqrt[3]{54} \approx 3.7798
\][/tex]
- Then multiply this result by 4:
[tex]\[
4 \times 3.7798 \approx 15.1191
\][/tex]
4. Combine the results:
- Add the evaluated terms from steps 1 and 2, and then subtract the term from step 3:
[tex]\[
18.8988 + 17.6389 - 15.1191 \approx 21.4187
\][/tex]
The simplified expression [tex]\(3 \sqrt[3]{250} + 7 \sqrt[3]{16} - 4 \sqrt[3]{54}\)[/tex] evaluates to approximately [tex]\(21.4187\)[/tex].
Thus, the final values are:
- [tex]\(3 \sqrt[3]{250} \approx 18.8988\)[/tex]
- [tex]\(7 \sqrt[3]{16} \approx 17.6389\)[/tex]
- [tex]\(4 \sqrt[3]{54} \approx 15.1191\)[/tex]
- Combined result: [tex]\(21.4187\)[/tex]
