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Let's break down the problem and simplify the expression step-by-step. The given expression is:

\[
4\sqrt{3} + 3\sqrt{12} - \sqrt{27}.
\]

### Step 1: Simplify Each Square Root
1. **\( \sqrt{12} \):**
   \[
   \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}.
   \]

2. **\( \sqrt{27} \):**
   \[
   \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}.
   \]

### Step 2: Substitute the Simplified Square Roots into the Expression
\[
4\sqrt{3} + 3\sqrt{12} - \sqrt{27} = 4\sqrt{3} + 3 \times 2\sqrt{3} - 3\sqrt{3}.
\]

### Step 3: Simplify the Expression
\[
4\sqrt{3} + 6\sqrt{3} - 3\sqrt{3}.
\]

Combine the terms:
\[
(4 + 6 - 3) \sqrt{3} = 7\sqrt{3}.
\]

So, the simplified form of the expression is \( 7\sqrt{3} \).

### Answer
The correct option is:
\[
\text{b. } 7\sqrt{3}.
\]

Would you like a detailed explanation of any step or have further questions?

Here are 5 related questions for further practice:
1. Simplify \( 5\sqrt{8} + 2\sqrt{18} \).
2. What is the simplified form of \( 3\sqrt{50} - 2\sqrt{8} + \sqrt{32} \)?
3. If \( x = \sqrt{75} + \sqrt{48} \), what is \( x \) in its simplest form?
4. How do you simplify \( 6\sqrt{27} + 4\sqrt{12} - 5\sqrt{3} \)?
5. Solve for \( x \) if \( 2x = 4\sqrt{5} - 2\sqrt{20} \).

**Tip:** Always look for square factors inside a square root to simplify it! For example, \( \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \).

Bentuk sederhana dari 4√3 + 3√12 − √27 adalah?

Learn how to simplify the radical expression 4√3 + 3√12 − √27 step by step. This solution covers key concepts in algebra, including radical simplification and square factors, making it suitable for students in Grades 9-11.

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