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Simplify: [tex][tex]$16 \sqrt{2} + 24 \sqrt{3} + 14 \sqrt{2} + 4 \sqrt{3}$[/tex][/tex]

A. [tex]$30 \sqrt{2} + 28 \sqrt{3}$[/tex]
B. [tex]$14 \sqrt{2} + 28 \sqrt{3}$[/tex]
C. [tex][tex]$30 \sqrt{3} + 28 \sqrt{2}$[/tex][/tex]
D. [tex]$30 \sqrt{2} - 28 \sqrt{3}$[/tex]

Sagot :

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]