`sqrt(86.49)+sqrt(5+k^(2))=12.3`. So k is equal to

Options

A. `sqrt(10)`
B. `2sqrt(5)`
C. `3sqrt(5)`
D. `2`

Answer

To solve the equation \( \sqrt{86.49} + \sqrt{5 + k^2} = 12.3 \), we will follow these steps:

### Step 1: Isolate the square root
We start by isolating the square root term involving \( k \):
\[ \sqrt{5 + k^2} = 12.3 - \sqrt{86.49} \]

### Step 2: Calculate \( \sqrt{86.49} \)
Next, we calculate \( \sqrt{86.49} \):
\[ \sqrt{86.49} = 9.3 \]

### Step 3: Substitute back into the equation
Now we substitute \( 9.3 \) back into the equation:
\[ \sqrt{5 + k^2} = 12.3 - 9.3 \]
This simplifies to:
\[ \sqrt{5 + k^2} = 3 \]

### Step 4: Square both sides
Next, we square both sides to eliminate the square root:
\[ 5 + k^2 = 3^2 \]
This simplifies to:
\[ 5 + k^2 = 9 \]

### Step 5: Solve for \( k^2 \)
Now, we solve for \( k^2 \):
\[ k^2 = 9 - 5 \]
This simplifies to:
\[ k^2 = 4 \]

### Step 6: Find \( k \)
Finally, we take the square root of both sides to find \( k \):
\[ k = \sqrt{4} \]
Thus, we find:
\[ k = 2 \quad \text{or} \quad k = -2 \]

### Final Answer
The value of \( k \) is \( 2 \) (considering only the positive root).

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