To simplify the expression [tex]\(16 \sqrt{2} + 24 \sqrt{3} + 14 \sqrt{2} + 4 \sqrt{3}\)[/tex], we can group and combine the like terms.
1. Identify the terms that involve [tex]\(\sqrt{2}\)[/tex] and [tex]\(\sqrt{3}\)[/tex]:
- Terms involving [tex]\(\sqrt{2}\)[/tex]: [tex]\(16 \sqrt{2}\)[/tex] and [tex]\(14 \sqrt{2}\)[/tex]
- Terms involving [tex]\(\sqrt{3}\)[/tex]: [tex]\(24 \sqrt{3}\)[/tex] and [tex]\(4 \sqrt{3}\)[/tex]
2. Combine the coefficients of the terms involving [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
16 \sqrt{2} + 14 \sqrt{2} = (16 + 14) \sqrt{2} = 30 \sqrt{2}
\][/tex]
3. Combine the coefficients of the terms involving [tex]\(\sqrt{3}\)[/tex]:
[tex]\[
24 \sqrt{3} + 4 \sqrt{3} = (24 + 4) \sqrt{3} = 28 \sqrt{3}
\][/tex]
4. Put the simplified expressions together:
[tex]\[
30 \sqrt{2} + 28 \sqrt{3}
\][/tex]
So, the simplified form of the given expression is [tex]\(30 \sqrt{2} + 28 \sqrt{3}\)[/tex].
Hence, the correct answer is:
A. [tex]\(30 \sqrt{2} + 28 \sqrt{3}\)[/tex]
