Perform the indicated operation. Express your answer in simplified form. Assume all variables represent positive real numbers. \( (\sqrt{p-9})^{2}=\square \)

When you square a square root, you typically get back the original expression inside the square root, as long as that expression is non-negative. Thus, \( (\sqrt{p-9})^{2} = p-9 \). Since we assume all variables represent positive real numbers, ensure that \( p > 9 \) to keep the expression valid and non-negative. Now, if you want to check your work, think about substituting values for \( p \). For instance, let \( p = 10 \). Then \( (\sqrt{10-9})^{2} = (\sqrt{1})^{2} = 1 \). This gives you confidence that your simplification is correct, and the final answer remains \( p - 9 \).