$\sqrt{x^2 - 2xy + y^2}$
To find the value of \(\sqrt{x^2 - 2xy + y^2}\), we can recognize this expression as a form of the perfect square trinomial, \((a-b)^2\), which is equal to \(a^2 - 2ab + b^2\).
- Identify the expression: Given \(x^2 - 2xy + y^2\), it matches the pattern \((x-y)^2\).
- Rewrite the expression using the formula: You can write the given expression as \((x-y)^2\).
- Substitute the values of \(x\) and \(y\): Here, \(x = 25\) and \(y = 13\). Therefore, we have \((25 - 13)^2\).
- Calculate the value inside the square root: Simplify \(25 - 13\) to get \(12\).
- Apply the square root: The square root of \((12)^2\) is \(12\).
Thus, the value of \(\sqrt{x^2 - 2xy + y^2}\) is 12.
The correct answer is: 12.
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