$ ext{If } \sqrt{3} = 1.732 ext{, then } \frac{1}{\sqrt{3}} ext{ is equal to :}$

Q: $\text{If } \sqrt{3} = 1.732 \text{, then } \frac{1}{\sqrt{3}} \text{ is equal to :}$

To determine the value of $\frac{1}{\sqrt{3}}$, we start with the given approximation $\sqrt{3} = 1.732$. 1. **Calculation of $\frac{1}{\sqrt{3}}$:** \[ \frac{1}{\sqrt{3}} = \frac{1}{1.732} \] Using a calculator or performing long division, we find: \[ \frac{1}{1.732} \approx 0.5773 \] Therefore, the correct value of $\frac{1}{\sqrt{3}}$ is approximately 0.5773, which matches Option 4. 2. **Explanation of why Option 4 is correct:** - The calculation above shows that $\frac{1}{\sqrt{3}}$ is approximately 0.5773. This directly supports Option 4 as the correct answer. 3. **Explanation of why the other options are incorrect:** - **Option 1 (0.866):** This value is incorrect because it is actually the approximate value of $\cos(30^\circ)$ or $\sin(60^\circ)$, not $\frac{1}{\sqrt{3}}$. - **Option 2 (0.433):** This value does not correspond to $\frac{1}{\sqrt{3}}$. It is not a standard approximation for any common trigonometric or mathematical constant related to $\sqrt{3}$. - **Option 3 (0.277):** This value is also incorrect. It is significantly lower than the actual value of $\frac{1}{\sqrt{3}}$ and does not relate to any standard mathematical constant involving $\sqrt{3}$. In conclusion, the correct answer is Option 4 (0.5773), as it accurately represents the value of $\frac{1}{\sqrt{3}}$ based on the given approximation of $\sqrt{3} = 1.732$.

Question

$	ext{If } \sqrt{3} = 1.732 	ext{, then } \frac{1}{\sqrt{3}} 	ext{ is equal to :}$

Accepted Answer

To determine the value of $\frac{1}{\sqrt{3}}$, we start with the given approximation $\sqrt{3} = 1.732$.

1. **Calculation of $\frac{1}{\sqrt{3}}$:**

$$
   \frac{1}{\sqrt{3}} = \frac{1}{1.732}
   $$

Using a calculator or performing long division, we find:

$$
   \frac{1}{1.732} \approx 0.5773
   $$

Therefore, the correct value of $\frac{1}{\sqrt{3}}$ is approximately 0.5773, which matches Option 4.

2. **Explanation of why Option 4 is correct:**

- The calculation above shows that $\frac{1}{\sqrt{3}}$ is approximately 0.5773. This directly supports Option 4 as the correct answer.

3. **Explanation of why the other options are incorrect:**

- **Option 1 (0.866):** This value is incorrect because it is actually the approximate value of $\cos(30^\circ)$ or $\sin(60^\circ)$, not $\frac{1}{\sqrt{3}}$.

- **Option 2 (0.433):** This value does not correspond to $\frac{1}{\sqrt{3}}$. It is not a standard approximation for any common trigonometric or mathematical constant related to $\sqrt{3}$.

- **Option 3 (0.277):** This value is also incorrect. It is significantly lower than the actual value of $\frac{1}{\sqrt{3}}$ and does not relate to any standard mathematical constant involving $\sqrt{3}$.

In conclusion, the correct answer is Option 4 (0.5773), as it accurately represents the value of $\frac{1}{\sqrt{3}}$ based on the given approximation of $\sqrt{3} = 1.732$.