If `9 sqrtx = sqrt12 + sqrt147` , then x = ? S

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the equation \( 9 \sqrt{x} = \sqrt{12} + \sqrt{147} \), we will follow these steps:

### Step 1: Simplify the right-hand side
First, we need to simplify \( \sqrt{12} \) and \( \sqrt{147} \).

- \( \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \)
- \( \sqrt{147} = \sqrt{49 \times 3} = \sqrt{49} \cdot \sqrt{3} = 7\sqrt{3} \)

Now, we can rewrite the equation:
\[ 9 \sqrt{x} = 2\sqrt{3} + 7\sqrt{3} \]

### Step 2: Combine like terms
Next, we combine the terms on the right-hand side:
\[ 2\sqrt{3} + 7\sqrt{3} = (2 + 7)\sqrt{3} = 9\sqrt{3} \]

Now the equation becomes:
\[ 9 \sqrt{x} = 9\sqrt{3} \]

### Step 3: Divide both sides by 9
To isolate \( \sqrt{x} \), we divide both sides of the equation by 9:
\[ \sqrt{x} = \sqrt{3} \]

### Step 4: Square both sides
Next, we square both sides to solve for \( x \):
\[ x = (\sqrt{3})^2 \]
\[ x = 3 \]

### Conclusion
Thus, the value of \( x \) is \( 3 \).

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