`sqrt(7921)xxsqrt(5329)-(78)^(2)=sqrt(?)+(19)^(2)`

Options

A. 2604
B. 2704
C. 2764
D. 2844

Explanation

To solve the equation \( \sqrt{7921} \times \sqrt{5329} - (78)^2 = \sqrt{?} + (19)^2 \), we will follow these steps:

### Step 1: Calculate \( \sqrt{7921} \)
First, we find the square root of 7921.
\[ \sqrt{7921} = 89 \]
**Hint:** To find the square root, check if the number is a perfect square by testing integers.

### Step 2: Calculate \( \sqrt{5329} \)
Next, we find the square root of 5329.
\[ \sqrt{5329} = 73 \]
**Hint:** Similar to step 1, check for perfect squares by testing integers.

### Step 3: Calculate \( (78)^2 \)
Now, we compute \( (78)^2 \).
\[ (78)^2 = 6084 \]
**Hint:** Squaring a number means multiplying it by itself.

### Step 4: Calculate \( (19)^2 \)
Next, we calculate \( (19)^2 \).
\[ (19)^2 = 361 \]
**Hint:** Again, squaring involves multiplying the number by itself.

### Step 5: Substitute and simplify the equation
Now we substitute the values we calculated into the equation:
\[ 89 \times 73 - 6084 = \sqrt{?} + 361 \]

### Step 6: Calculate \( 89 \times 73 \)
Now we calculate \( 89 \times 73 \):
\[ 89 \times 73 = 6497 \]
**Hint:** Use the multiplication method or break it down into smaller parts for easier calculation.

### Step 7: Substitute and simplify further
Now we substitute this back into the equation:
\[ 6497 - 6084 = \sqrt{?} + 361 \]

### Step 8: Calculate \( 6497 - 6084 \)
Now we perform the subtraction:
\[ 6497 - 6084 = 413 \]
**Hint:** Subtract the smaller number from the larger number directly.

### Step 9: Set up the equation for \( \sqrt{?} \)
Now we have:
\[ 413 = \sqrt{?} + 361 \]

### Step 10: Isolate \( \sqrt{?} \)
To isolate \( \sqrt{?} \), we subtract 361 from both sides:
\[ \sqrt{?} = 413 - 361 \]

### Step 11: Calculate \( 413 - 361 \)
Now we perform the subtraction:
\[ 413 - 361 = 52 \]
**Hint:** Again, subtract the smaller number from the larger number.

### Step 12: Square both sides to find \( ? \)
Now we square both sides to find \( ? \):
\[ ? = 52^2 \]
Calculating \( 52^2 \):
\[ 52^2 = 2704 \]

### Final Answer
Thus, the value of \( ? \) is:
\[ \boxed{2704} \]