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Find the sum: [tex]\(\sqrt{3} + 11\sqrt{12}\)[/tex]

A. [tex]\(15\sqrt{15}\)[/tex]

B. [tex]\(15\sqrt{3}\)[/tex]

C. [tex]\(26\sqrt{3}\)[/tex]

D. [tex]\(48\sqrt{3}\)[/tex]

Sagot :

GinnyAnswer
To find the sum [tex]\(\sqrt{3} + 11\sqrt{12}\)[/tex], we need to simplify the terms and then combine them:

1. Simplify [tex]\(\sqrt{12}\)[/tex]:
[tex]\[\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}\][/tex]

2. Substitute [tex]\(\sqrt{12}\)[/tex] in the given expression:
[tex]\[11\sqrt{12} = 11 \cdot 2\sqrt{3} = 22\sqrt{3}\][/tex]

3. Combine the simplified terms [tex]\(\sqrt{3}\)[/tex] and [tex]\(22\sqrt{3}\)[/tex]:
[tex]\[\sqrt{3} + 22\sqrt{3} = (1 + 22)\sqrt{3} = 23\sqrt{3}\][/tex]

Therefore, the sum [tex]\(\sqrt{3} + 11\sqrt{12}\)[/tex] is [tex]\(23\sqrt{3}\)[/tex].

So, the correct answer is:
[tex]\[ \boxed{23\sqrt{3}} \][/tex]
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