The value of $\frac{1}{\sqrt{2}}$ is:

Q: The value of $\frac{1}{\sqrt{2}}$ is:

The value of $\frac{1}{\sqrt{2}}$ can be simplified to $\frac{\sqrt{2}}{2}$. Let's go through the explanation to understand why Option 3 is correct and why the other options are incorrect. 1. **Explanation for Option 3 ($\frac{\sqrt{2}}{2}$):** To simplify $\frac{1}{\sqrt{2}}$, we can multiply both the numerator and the denominator by $\sqrt{2}$ to rationalize the denominator: \[ \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2} \] This process eliminates the square root from the denominator, resulting in $\frac{\sqrt{2}}{2}$. Therefore, Option 3 is the correct answer. 2. **Explanation for why the other options are incorrect:** - **Option 1 ($\sqrt{2}$):** $\sqrt{2}$ is not equivalent to $\frac{1}{\sqrt{2}}$. In fact, $\sqrt{2}$ is the reciprocal of $\frac{1}{\sqrt{2}}$, not the same value. Therefore, this option is incorrect. - **Option 2 (2):** The value 2 is not related to $\frac{1}{\sqrt{2}}$ in any direct way. Simplifying $\frac{1}{\sqrt{2}}$ does not result in 2, so this option is incorrect. - **Option 4 ($\frac{2}{\sqrt{2}}$):** $\frac{2}{\sqrt{2}}$ can be simplified by rationalizing the denominator: \[ \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2} \] This simplification shows that $\frac{2}{\sqrt{2}}$ equals $\sqrt{2}$, not $\frac{1}{\sqrt{2}}$. Therefore, this option is incorrect. In conclusion, the correct answer is Option 3, $\frac{\sqrt{2}}{2}$, as it accurately represents the simplified form of $\frac{1}{\sqrt{2}}$.

Question

Accepted Answer

The value of $\frac{1}{\sqrt{2}}$ can be simplified to $\frac{\sqrt{2}}{2}$. Let's go through the explanation to understand why Option 3 is correct and why the other options are incorrect.

1. **Explanation for Option 3 ($\frac{\sqrt{2}}{2}$):**

To simplify $\frac{1}{\sqrt{2}}$, we can multiply both the numerator and the denominator by $\sqrt{2}$ to rationalize the denominator:

$$
   \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}
   $$

This process eliminates the square root from the denominator, resulting in $\frac{\sqrt{2}}{2}$. Therefore, Option 3 is the correct answer.

2. **Explanation for why the other options are incorrect:**

- **Option 1 ($\sqrt{2}$):** 
     $\sqrt{2}$ is not equivalent to $\frac{1}{\sqrt{2}}$. In fact, $\sqrt{2}$ is the reciprocal of $\frac{1}{\sqrt{2}}$, not the same value. Therefore, this option is incorrect.

- **Option 2 (2):**
     The value 2 is not related to $\frac{1}{\sqrt{2}}$ in any direct way. Simplifying $\frac{1}{\sqrt{2}}$ does not result in 2, so this option is incorrect.

- **Option 4 ($\frac{2}{\sqrt{2}}$):**
     $\frac{2}{\sqrt{2}}$ can be simplified by rationalizing the denominator:

$$
     \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2}
     $$

This simplification shows that $\frac{2}{\sqrt{2}}$ equals $\sqrt{2}$, not $\frac{1}{\sqrt{2}}$. Therefore, this option is incorrect.

In conclusion, the correct answer is Option 3, $\frac{\sqrt{2}}{2}$, as it accurately represents the simplified form of $\frac{1}{\sqrt{2}}$.