If `9sqrt(x)=sqrt(12)+sqrt(147)` , then x `=?`

Options

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

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 will 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 the terms on the right-hand side
Now, we can combine the terms on the right side:

\[ 2\sqrt{3} + 7\sqrt{3} = (2 + 7)\sqrt{3} = 9\sqrt{3} \]

So now our equation looks like this:

\[ 9\sqrt{x} = 9\sqrt{3} \]

### Step 3: Divide both sides by 9
Next, we can divide both sides of the equation by 9:

\[ \sqrt{x} = \sqrt{3} \]

### Step 4: Square both sides
Now, we will square both sides to solve for \( x \):

\[ x = (\sqrt{3})^2 \]

\[ x = 3 \]

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

### Final Answer
\[ x = 3 \]

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