#### Answer

$p=\pm5\sqrt{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
p^2-50=0
,$ use the properties of equality and express the equation in the form $x^2=c.$ Then take the square root of both sides (Square Root Property) and simplify the resulting radical.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
p^2=50
.\end{array}
Taking the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{array}{l}\require{cancel}
p=\pm\sqrt{50}
.\end{array}
Writing the radicand as an expression that contains a factor that is a perfect power of the index and then extracting the root of that factor result to
\begin{array}{l}\require{cancel}
p=\pm\sqrt{25\cdot2}
\\\\
p=\pm\sqrt{(5)^2\cdot2}
\\\\
p=\pm5\sqrt{2}
.\end{array}