Find the value of `sqrt(0.5)` without long division method

Options

A. 0.897
B. 0.787
C. 0.947
D. 0.707

Answer

To find the value of \( \sqrt{0.5} \) without using the long division method, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite \( 0.5 \) as a fraction**:
\[ 0.5 = \frac{1}{2} \]

2. **Apply the square root to the fraction**:
\[ \sqrt{0.5} = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} \]

3. **Calculate the square root of 1**:
\[ \sqrt{1} = 1 \]

4. **Now we need to find \( \sqrt{2} \)**:
The approximate value of \( \sqrt{2} \) is \( 1.414 \).

5. **Substitute back into the fraction**:
\[ \sqrt{0.5} = \frac{1}{\sqrt{2}} \approx \frac{1}{1.414} \]

6. **Perform the division**:
\[ \frac{1}{1.414} \approx 0.707 \]

7. **Final result**:
\[ \sqrt{0.5} \approx 0.707 \]

### Conclusion:
The value of \( \sqrt{0.5} \) is approximately \( 0.707 \).