`sqrt(104.04)+sqrt(1.0404)+sqrt(0.010404)` is equal to

Options

A. 0.306
B. 0.0306
C. 11.122
D. 11.322

Answer

To solve the expression \( \sqrt{104.04} + \sqrt{1.0404} + \sqrt{0.010404} \), we will calculate each square root step by step.

### Step 1: Calculate \( \sqrt{104.04} \)

To find \( \sqrt{104.04} \), we can express it as:
\[ \sqrt{104.04} = \sqrt{10404 / 100} = \frac{\sqrt{10404}}{10} \]
Now, we need to find \( \sqrt{10404} \).

Calculating \( 102^2 \):
\[ 102^2 = 10404 \]
Thus,
\[ \sqrt{10404} = 102 \]
So,
\[ \sqrt{104.04} = \frac{102}{10} = 10.2 \]

### Step 2: Calculate \( \sqrt{1.0404} \)

Next, we calculate \( \sqrt{1.0404} \):
\[ \sqrt{1.0404} = \sqrt{10404 / 10000} = \frac{\sqrt{10404}}{100} \]
Since we already found \( \sqrt{10404} = 102 \):
\[ \sqrt{1.0404} = \frac{102}{100} = 1.02 \]

### Step 3: Calculate \( \sqrt{0.010404} \)

Now, we calculate \( \sqrt{0.010404} \):
\[ \sqrt{0.010404} = \sqrt{10404 / 1000000} = \frac{\sqrt{10404}}{1000} \]
Using \( \sqrt{10404} = 102 \):
\[ \sqrt{0.010404} = \frac{102}{1000} = 0.102 \]

### Step 4: Add the results together

Now we add all the results:
\[ \sqrt{104.04} + \sqrt{1.0404} + \sqrt{0.010404} = 10.2 + 1.02 + 0.102 \]

Aligning the decimal points for addition:
```
10.200
+ 1.020
+ 0.102
---------
11.322
```

Thus, the final result is:
\[ \sqrt{104.04} + \sqrt{1.0404} + \sqrt{0.010404} = 11.322 \]

### Conclusion

The answer is \( 11.322 \).