If `sqrt(5 + root(3)(x)) = 3`, then the value of x is :

Options

A. 9
B. 27
C. 64
D. 343

Answer

To solve the equation \( \sqrt{5 + \sqrt[3]{x}} = 3 \), we will follow these steps:

### Step 1: Isolate the square root
We start with the equation:
\[ \sqrt{5 + \sqrt[3]{x}} = 3 \]
To eliminate the square root, we square both sides:
\[ 5 + \sqrt[3]{x} = 3^2 \]
This simplifies to:
\[ 5 + \sqrt[3]{x} = 9 \]

### Step 2: Solve for the cube root
Next, we isolate \( \sqrt[3]{x} \) by subtracting 5 from both sides:
\[ \sqrt[3]{x} = 9 - 5 \]
This simplifies to:
\[ \sqrt[3]{x} = 4 \]

### Step 3: Cube both sides
To find \( x \), we cube both sides of the equation:
\[ x = 4^3 \]
Calculating \( 4^3 \):
\[ x = 64 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{64} \]

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