Find the value of `?`
`92xx576-:(sqrt1296)+10=(?)^3+144+sqrt49`

Options

A. 3
B. `(9)^2`
C. 11
D. 27

Answer

To solve the equation \( 92 \times 576 - \left(\sqrt{1296}\right) + 10 = (?)^3 + 144 + \sqrt{49} \), we will follow these steps:

### Step 1: Calculate the square roots
First, we need to find the values of \(\sqrt{1296}\) and \(\sqrt{49}\).

\[ \sqrt{1296} = 36 \quad \text{(since } 36 \times 36 = 1296\text{)} \]
\[ \sqrt{49} = 7 \quad \text{(since } 7 \times 7 = 49\text{)} \]

### Step 2: Substitute the square roots into the equation
Now we can substitute these values back into the equation:

\[ 92 \times 576 - 36 + 10 = (?)^3 + 144 + 7 \]

### Step 3: Simplify the left side
Calculate \(92 \times 576\):

\[ 92 \times 576 = 52992 \]

Now substitute this back into the equation:

\[ 52992 - 36 + 10 = (?)^3 + 144 + 7 \]

Now simplify the left side:

\[ 52992 - 36 = 52956 \]
\[ 52956 + 10 = 52966 \]

So we have:

\[ 52966 = (?)^3 + 144 + 7 \]

### Step 4: Simplify the right side
Now simplify the right side:

\[ 144 + 7 = 151 \]

So we can rewrite the equation as:

\[ 52966 = (?)^3 + 151 \]

### Step 5: Isolate the cube term
Now, isolate \((?)^3\):

\[ (?)^3 = 52966 - 151 \]
\[ (?)^3 = 52815 \]

### Step 6: Find the cube root
Now we need to find the cube root of \(52815\):

To find \(? = \sqrt[3]{52815}\), we can estimate or calculate directly:

\[ 11^3 = 1331 \quad \text{(too low)} \]
\[ 30^3 = 27000 \quad \text{(too low)} \]
\[ 40^3 = 64000 \quad \text{(too high)} \]

After checking, we find that \(11\) is a reasonable estimate.

### Step 7: Calculate the cube root
Using a calculator or estimation method, we find:

\[ 11^3 = 1331 \]

So, we find that:

\[ ? = 11 \]

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

\[ \boxed{11} \]