If `sqrt(10+root(3)(x))=4`, then what is the value of x ?

Options

A. 150
B. 216
C. 316
D. 450

Answer

To solve the equation \( \sqrt{10 + 3\sqrt{x}} = 4 \), we will follow these steps:

### Step 1: Square both sides of the equation
To eliminate the square root, we square both sides of the equation:

\[ (\sqrt{10 + 3\sqrt{x}})^2 = 4^2 \]

This simplifies to:

\[ 10 + 3\sqrt{x} = 16 \]

### Step 2: Isolate the term with the square root
Next, we isolate the term containing \( \sqrt{x} \):

\[ 3\sqrt{x} = 16 - 10 \]

This simplifies to:

\[ 3\sqrt{x} = 6 \]

### Step 3: Solve for \( \sqrt{x} \)
Now, we divide both sides by 3:

\[ \sqrt{x} = \frac{6}{3} \]

This simplifies to:

\[ \sqrt{x} = 2 \]

### Step 4: Square both sides again to solve for \( x \)
To find \( x \), we square both sides again:

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

This gives us:

\[ x = 4 \]

### Final Answer
Thus, the value of \( x \) is:

\[ \boxed{4} \]

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