To solve the expression [tex]\(7 \sqrt[3]{31} + 5 \sqrt[3]{24} - 2 \sqrt[3]{345}\)[/tex], we can break it down into three main terms and simplify each one separately.
1. First Term:
[tex]\[
7 \sqrt[3]{31}
\][/tex]
The value of [tex]\(\sqrt[3]{31}\)[/tex] is approximately 3.141. Multiplying this by 7 gives:
[tex]\[
7 \sqrt[3]{31} \approx 7 \times 3.141 = 21.990
\][/tex]
2. Second Term:
[tex]\[
5 \sqrt[3]{24}
\][/tex]
The value of [tex]\(\sqrt[3]{24}\)[/tex] is approximately 2.884. Multiplying this by 5 gives:
[tex]\[
5 \sqrt[3]{24} \approx 5 \times 2.884 = 14.422
\][/tex]
3. Third Term:
[tex]\[
-2 \sqrt[3]{345}
\][/tex]
The value of [tex]\(\sqrt[3]{345}\)[/tex] is approximately 7.014. Multiplying this by -2 gives:
[tex]\[
-2 \sqrt[3]{345} \approx -2 \times 7.014 = -14.027
\][/tex]
Finally, we sum these three results together:
[tex]\[
21.990 + 14.422 - 14.027 = 22.385
\][/tex]
Therefore, the simplified value of the expression [tex]\(7 \sqrt[3]{31} + 5 \sqrt[3]{24} - 2 \sqrt[3]{345}\)[/tex] is approximately:
[tex]\[
22.385
\][/tex]
