To simplify the expression [tex]\(3 \sqrt{7} + 3 \sqrt{63}\)[/tex], follow these steps:
1. Simplify [tex]\(\sqrt{63}\)[/tex]:
- Notice that [tex]\(63\)[/tex] can be factored into [tex]\(9 \times 7\)[/tex].
- Therefore, [tex]\(\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7}\)[/tex].
- Since [tex]\(\sqrt{9} = 3\)[/tex], it follows that [tex]\(\sqrt{63} = 3 \sqrt{7}\)[/tex].
2. Substitute back into the original expression:
- Replace [tex]\(\sqrt{63}\)[/tex] with [tex]\(3 \sqrt{7}\)[/tex].
- The expression becomes [tex]\(3 \sqrt{7} + 3 (3 \sqrt{7})\)[/tex].
3. Combine terms:
- Simplify the expression inside the parentheses first: [tex]\(3 (3 \sqrt{7}) = 9 \sqrt{7}\)[/tex].
- Thus, the expression becomes [tex]\(3 \sqrt{7} + 9 \sqrt{7}\)[/tex].
4. Add like terms:
- Both terms contain [tex]\(\sqrt{7}\)[/tex], so they can be combined like regular algebraic terms.
- Combine [tex]\(3 \sqrt{7}\)[/tex] and [tex]\(9 \sqrt{7}\)[/tex] to get [tex]\((3 + 9) \sqrt{7} = 12 \sqrt{7}\)[/tex].
Hence, the simplified form of the expression [tex]\(3 \sqrt{7} + 3 \sqrt{63}\)[/tex] is [tex]\(12 \sqrt{7}\)[/tex].
The correct answer is:
A. [tex]\(12 \sqrt{7}\)[/tex]
