#### Answer

$p=\pm5\sqrt{2}$

#### Work Step by Step

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}