If x = 1.1 then what is the value of ` sqrt(4x^2 - 4x+1)?`

Options

A. 1.21
B. 1.331
C. 2.21
D. 1.2

Answer

To solve the problem, we need to find the value of \( \sqrt{4x^2 - 4x + 1} \) when \( x = 1.1 \).

### Step-by-step Solution:

1. **Substitute the value of x**:
\[ x = 1.1 \]
We substitute this value into the expression:
\[ \sqrt{4(1.1)^2 - 4(1.1) + 1} \]

2. **Calculate \( (1.1)^2 \)**:
\[ (1.1)^2 = 1.21 \]
Now substitute this back into the expression:
\[ \sqrt{4(1.21) - 4(1.1) + 1} \]

3. **Multiply by 4**:
\[ 4(1.21) = 4.84 \]
Now the expression becomes:
\[ \sqrt{4.84 - 4(1.1) + 1} \]

4. **Calculate \( 4(1.1) \)**:
\[ 4(1.1) = 4.4 \]
Substitute this value into the expression:
\[ \sqrt{4.84 - 4.4 + 1} \]

5. **Simplify inside the square root**:
\[ 4.84 - 4.4 = 0.44 \]
Now add 1:
\[ 0.44 + 1 = 1.44 \]
So now we have:
\[ \sqrt{1.44} \]

6. **Calculate the square root**:
\[ \sqrt{1.44} = 1.2 \]

Thus, the final answer is:
\[ \boxed{1.2} \]