If `sqrt(3)=1.732` then the approximate value of `1/sqrt(3)` is

Options

A. 0.617
B. 0.313
C. 0.577
D. 0.173

Answer

To find the approximate value of \( \frac{1}{\sqrt{3}} \) given that \( \sqrt{3} = 1.732 \), we can follow these steps:

### Step-by-Step Solution:

1. **Start with the expression**: We need to calculate \( \frac{1}{\sqrt{3}} \).

2. **Multiply by \( \frac{\sqrt{3}}{\sqrt{3}} \)**: To simplify the fraction, we can multiply the numerator and denominator by \( \sqrt{3} \):
\[ \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3} \]

3. **Substitute the value of \( \sqrt{3} \)**: We know that \( \sqrt{3} = 1.732 \), so we can substitute this value into the expression:
\[ \frac{\sqrt{3}}{3} = \frac{1.732}{3} \]

4. **Perform the division**: Now, we need to divide \( 1.732 \) by \( 3 \):
\[ 1.732 \div 3 \]

Performing the division:
- \( 3 \) goes into \( 1 \) zero times.
- \( 3 \) goes into \( 17 \) five times (since \( 3 \times 5 = 15 \)).
- Subtract \( 15 \) from \( 17 \) to get \( 2 \).
- Bring down the next digit \( 3 \) to make it \( 23 \).
- \( 3 \) goes into \( 23 \) seven times (since \( 3 \times 7 = 21 \)).
- Subtract \( 21 \) from \( 23 \) to get \( 2 \).
- Bring down the next digit \( 2 \) to make it \( 22 \).
- \( 3 \) goes into \( 22 \) seven times (since \( 3 \times 7 = 21 \)).
- Subtract \( 21 \) from \( 22 \) to get \( 1 \).

Thus, we have:
\[ 1.732 \div 3 \approx 0.577 \]

5. **Final result**: Therefore, the approximate value of \( \frac{1}{\sqrt{3}} \) is \( 0.577 \).