`sqrt(1089)`+`sqrt(289)`=`sqrt(?)`

Options

A. 625
B. 50
C. 2500
D. 1378

Answer

To solve the equation \( \sqrt{1089} + \sqrt{289} = \sqrt{?} \), we will follow these steps:

### Step 1: Calculate \( \sqrt{1089} \)
First, we need to find the square root of 1089.

To do this, we can factor 1089:
- 1089 = 33 × 33
- Therefore, \( \sqrt{1089} = 33 \).

### Step 2: Calculate \( \sqrt{289} \)
Next, we calculate the square root of 289.

To factor 289:
- 289 = 17 × 17
- Therefore, \( \sqrt{289} = 17 \).

### Step 3: Add the results
Now we can add the two square roots we calculated:
\[ \sqrt{1089} + \sqrt{289} = 33 + 17 = 50. \]

### Step 4: Set up the equation
We now have:
\[ 50 = \sqrt{?}. \]

### Step 5: Square both sides
To find the value of the question mark, we square both sides:
\[ 50^2 = ?. \]
Calculating \( 50^2 \):
\[ 50^2 = 2500. \]

### Conclusion
Thus, we find that:
\[ \sqrt{1089} + \sqrt{289} = \sqrt{2500}. \]

The final answer is:
\[ ? = 2500. \]

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