If w is a positive number and `w^(2)=2`, then `w^(2)=`

Options

A. `sqrt(2)`
B. `2sqrt(2)`
C. `4`
D. `3sqrt(2)`

Answer

To solve the problem step by step, we start with the given information:

1. **Given Information**: We know that \( w^2 = 2 \) and \( w \) is a positive number.

2. **Finding the Value of \( w \)**: Since \( w^2 = 2 \), we can find \( w \) by taking the square root of both sides.
\[ w = \sqrt{2} \]

3. **Finding \( w^3 \)**: We need to find \( w^3 \). We can express \( w^3 \) in terms of \( w^2 \) and \( w \):
\[ w^3 = w^2 \cdot w \]

4. **Substituting Known Values**: We already know that \( w^2 = 2 \) and \( w = \sqrt{2} \). We can substitute these values into the equation:
\[ w^3 = 2 \cdot \sqrt{2} \]

5. **Final Calculation**: Therefore, the value of \( w^3 \) is:
\[ w^3 = 2\sqrt{2} \]

Thus, the final answer is:
\[ w^3 = 2\sqrt{2} \]