The simplified value of `sqrt(900) + sqrt(0.09) - sqrt(0.000009)` is

Options

A. 30.27
B. 20.297
C. 30.097
D. 30.197

Answer

To simplify the expression \( \sqrt{900} + \sqrt{0.09} - \sqrt{0.000009} \), we will follow these steps:

### Step 1: Simplify \( \sqrt{900} \)
The square root of 900 can be calculated as follows:
\[ \sqrt{900} = 30 \]
**Hint:** Remember that \( 30 \times 30 = 900 \).

### Step 2: Simplify \( \sqrt{0.09} \)
Next, we simplify \( \sqrt{0.09} \):
\[ \sqrt{0.09} = \sqrt{\frac{9}{100}} = \frac{\sqrt{9}}{\sqrt{100}} = \frac{3}{10} = 0.3 \]
**Hint:** You can express 0.09 as a fraction to make it easier to simplify.

### Step 3: Simplify \( \sqrt{0.000009} \)
Now, we simplify \( \sqrt{0.000009} \):
\[ \sqrt{0.000009} = \sqrt{\frac{9}{1000000}} = \frac{\sqrt{9}}{\sqrt{1000000}} = \frac{3}{1000} = 0.003 \]
**Hint:** Again, expressing the decimal as a fraction can help in simplification.

### Step 4: Combine the results
Now we can combine all the simplified values:
\[ \sqrt{900} + \sqrt{0.09} - \sqrt{0.000009} = 30 + 0.3 - 0.003 \]
Calculating this step-by-step:
1. First, add \( 30 + 0.3 = 30.3 \).
2. Then, subtract \( 0.003 \):
\[ 30.3 - 0.003 = 30.297 \]

### Final Result
Thus, the simplified value of the expression is:
\[ \boxed{30.297} \]