To solve the expression [tex]\(6 \sqrt[3]{375} - 2 \sqrt[3]{192}\)[/tex], let's proceed with a step-by-step approach:
### Step 1: Calculate the Cubic Roots
1. Cubic Root of 375:
[tex]\[
\sqrt[3]{375} \approx 7.211247851537041
\][/tex]
2. Cubic Root of 192:
[tex]\[
\sqrt[3]{192} \approx 5.768998281229633
\][/tex]
### Step 2: Apply the Coefficients
1. First Term:
[tex]\[
6 \sqrt[3]{375} = 6 \cdot 7.211247851537041 \approx 43.267487109222245
\][/tex]
2. Second Term:
[tex]\[
-2 \sqrt[3]{192} = -2 \cdot 5.768998281229633 \approx -11.537996562459266
\][/tex]
### Step 3: Sum the Terms
[tex]\[
43.267487109222245 + (-11.537996562459266) = 43.267487109222245 - 11.537996562459266 \approx 31.729490546762978
\][/tex]
### Final Statement
The value of the expression [tex]\(6 \sqrt[3]{375} - 2 \sqrt[3]{192}\)[/tex] is approximately [tex]\(31.729490546762978\)[/tex].
