If `p(x)=x^(2)-2sqrt(2)x+1`, then `p(2sqrt(2))`=

Answer

To solve the problem, we need to evaluate the polynomial \( p(x) = x^2 - 2\sqrt{2}x + 1 \) at \( x = 2\sqrt{2} \).

### Step-by-Step Solution:

1. **Substitute \( x \) with \( 2\sqrt{2} \)**:
\[ p(2\sqrt{2}) = (2\sqrt{2})^2 - 2\sqrt{2}(2\sqrt{2}) + 1 \]

2. **Calculate \( (2\sqrt{2})^2 \)**:
\[ (2\sqrt{2})^2 = 2^2 \cdot (\sqrt{2})^2 = 4 \cdot 2 = 8 \]

3. **Calculate \( -2\sqrt{2}(2\sqrt{2}) \)**:
\[ -2\sqrt{2}(2\sqrt{2}) = -4 \cdot 2 = -8 \]

4. **Combine the results**:
\[ p(2\sqrt{2}) = 8 - 8 + 1 \]

5. **Simplify the expression**:
\[ p(2\sqrt{2}) = 0 + 1 = 1 \]

Thus, the value of \( p(2\sqrt{2}) \) is \( 1 \).

### Final Answer:
\[ p(2\sqrt{2}) = 1 \]