Chapter 11 - Quadratic Functions and Equations - 11.1 Quadratic Equations - 11.1 Exercise Set - Page 706: 9

$p=\pm5\sqrt{2}$

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle). Therefore, the solutions to the given equation, $ p^2-50=0 ,$ are \begin{array}{l}\require{cancel} p^2=50 \\\\ p=\pm\sqrt{50} \\\\ p=\pm\sqrt{25\cdot2} \\\\ p=\pm\sqrt{(5)^2\cdot2} \\\\ p=\pm5\sqrt{2} .\end{array}