If `sqrt(1 + (x)/(961)) = 32/31` , then the value of x is

Options

A. 63
B. 61
C. 65
D. 64

Answer

To solve the equation \( \sqrt{1 + \frac{x}{961}} = \frac{32}{31} \), we will follow these steps:

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

\[ \left(\sqrt{1 + \frac{x}{961}}\right)^2 = \left(\frac{32}{31}\right)^2 \]

This simplifies to:

\[ 1 + \frac{x}{961} = \frac{32^2}{31^2} \]

### Step 2: Calculate \( \frac{32^2}{31^2} \)
Now we calculate \( 32^2 \) and \( 31^2 \):

\[ 32^2 = 1024 \quad \text{and} \quad 31^2 = 961 \]

So, we have:

\[ 1 + \frac{x}{961} = \frac{1024}{961} \]

### Step 3: Isolate \( \frac{x}{961} \)
Next, we will isolate \( \frac{x}{961} \) by subtracting 1 from both sides. Since 1 can be expressed as \( \frac{961}{961} \):

\[ \frac{x}{961} = \frac{1024}{961} - \frac{961}{961} \]

This simplifies to:

\[ \frac{x}{961} = \frac{1024 - 961}{961} = \frac{63}{961} \]

### Step 4: Solve for \( x \)
Now, we will multiply both sides by 961 to solve for \( x \):

\[ x = 63 \]

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

\[ \boxed{63} \]