To simplify the given expression [tex]\(10 \sqrt{3x} + 4 \sqrt{3x} + 5 \sqrt{3x}\)[/tex], follow these steps:
1. Identify Like Terms:
Notice that each term contains the same radical part, which is [tex]\(\sqrt{3x}\)[/tex].
2. Combine the Coefficients:
Since [tex]\(\sqrt{3x}\)[/tex] is a common factor in all terms, we can factor it out:
[tex]\[
10 \sqrt{3x} + 4 \sqrt{3x} + 5 \sqrt{3x} = (10 + 4 + 5) \sqrt{3x}
\][/tex]
3. Sum the Coefficients:
Add the coefficients [tex]\(10\)[/tex], [tex]\(4\)[/tex], and [tex]\(5\)[/tex]:
[tex]\[
10 + 4 + 5 = 19
\][/tex]
4. Construct the Simplified Expression:
Multiply the sum of the coefficients by the common radical part:
[tex]\[
19 \sqrt{3x}
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
19 \sqrt{3x}
\][/tex]
The correct answer is:
[tex]\[
\boxed{19 \sqrt{3x}}
\][/tex]
