`sqrt(11449)xxsqrt(6241)-54^(2)=?+74^(2)`

Options

A. 48
B. 61
C. 56
D. 72

Explanation

To solve the equation \( \sqrt{11449} \times \sqrt{6241} - 54^2 = ? + 74^2 \), we will follow these steps:

### Step 1: Calculate \( \sqrt{11449} \)
To find \( \sqrt{11449} \), we can check for perfect squares.

Calculating:
\[ \sqrt{11449} = 107 \]

### Step 2: Calculate \( \sqrt{6241} \)
Next, we calculate \( \sqrt{6241} \).

Calculating:
\[ \sqrt{6241} = 79 \]

### Step 3: Multiply the square roots
Now we multiply the results from Step 1 and Step 2.

Calculating:
\[ \sqrt{11449} \times \sqrt{6241} = 107 \times 79 \]

Calculating \( 107 \times 79 \):
\[ 107 \times 79 = 8463 \]

### Step 4: Calculate \( 54^2 \)
Next, we calculate \( 54^2 \).

Calculating:
\[ 54^2 = 2916 \]

### Step 5: Substitute values into the equation
Now we substitute the values back into the equation:

\[ 8463 - 2916 = ? + 74^2 \]

### Step 6: Calculate \( 74^2 \)
We need to calculate \( 74^2 \).

Calculating:
\[ 74^2 = 5476 \]

### Step 7: Rearranging the equation
Now we can rearrange the equation to isolate \( ? \):

\[ 8463 - 2916 = ? + 5476 \]

Calculating the left side:
\[ 8463 - 2916 = 5547 \]

So, we have:
\[ 5547 = ? + 5476 \]

### Step 8: Solve for \( ? \)
Now, we solve for \( ? \):

\[ ? = 5547 - 5476 \]

Calculating:
\[ ? = 71 \]

### Final Answer
Thus, the final answer is:
\[ ? = 71 \]

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