If a = 0.1039 then the value of ` sqrt(4a^(2) - 4a + 1) + 3a ` is

Options

A. `0.1039`
B. `0.2078`
C. `1.1039`
D. `2.1039`

Answer

To solve the expression \( \sqrt{4a^2 - 4a + 1} + 3a \) given that \( a = 0.1039 \), we can follow these steps:

### Step 1: Substitute the value of \( a \)
First, we substitute \( a \) with \( 0.1039 \) in the expression.

\[ \sqrt{4(0.1039)^2 - 4(0.1039) + 1} + 3(0.1039) \]

### Step 2: Calculate \( 4a^2 \)
Calculate \( 4(0.1039)^2 \):

\[ 4(0.1039)^2 = 4 \times 0.01079621 \approx 0.04318484 \]

### Step 3: Calculate \( -4a \)
Calculate \( -4(0.1039) \):

\[ -4(0.1039) = -0.4156 \]

### Step 4: Combine the terms inside the square root
Now we combine the terms inside the square root:

\[ 0.04318484 - 0.4156 + 1 \]

Calculating this step by step:

1. \( 0.04318484 - 0.4156 \approx -0.37241516 \)
2. \( -0.37241516 + 1 \approx 0.62758484 \)

### Step 5: Take the square root
Now we take the square root of the result:

\[ \sqrt{0.62758484} \approx 0.791 \]

### Step 6: Calculate \( 3a \)
Now calculate \( 3(0.1039) \):

\[ 3(0.1039) = 0.3177 \]

### Step 7: Add the results
Finally, we add the results from Step 5 and Step 6:

\[ 0.791 + 0.3177 \approx 1.1087 \]

### Final Answer
Thus, the value of \( \sqrt{4a^2 - 4a + 1} + 3a \) is approximately \( 1.1087 \).

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