What will come in place of question mark (?) .
`33 xx 33 - ?^(1//2) + 10 xx 10 = 1068`

Options

A. `11^4`
B. `11^5`
C. `10^4`
D. `10^5`

Answer

To solve the equation \( 33 \times 33 - ?^{(1/2)} + 10 \times 10 = 1068 \), we can follow these steps:

### Step 1: Rewrite the equation
We can rewrite the equation using squares:
\[ 33^2 - ?^{(1/2)} + 10^2 = 1068 \]

### Step 2: Calculate the squares
Calculate \( 33^2 \) and \( 10^2 \):
\[ 33^2 = 1089 \]
\[ 10^2 = 100 \]

### Step 3: Substitute the squares back into the equation
Now substitute these values back into the equation:
\[ 1089 - ?^{(1/2)} + 100 = 1068 \]

### Step 4: Combine the constants
Combine \( 1089 \) and \( 100 \):
\[ 1189 - ?^{(1/2)} = 1068 \]

### Step 5: Isolate the square root term
Now, isolate \( ?^{(1/2)} \):
\[ 1189 - 1068 = ?^{(1/2)} \]
\[ 121 = ?^{(1/2)} \]

### Step 6: Square both sides to find ?
Square both sides to eliminate the square root:
\[ ? = 121^2 \]

### Step 7: Calculate \( 121^2 \)
Now calculate \( 121^2 \):
\[ 121^2 = 14641 \]

### Final Answer
Thus, the value of the question mark \( ? \) is:
\[ ? = 14641 \]

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