Answer
$p=12$
Check:
$\sqrt {\frac{12}{2}-2}=\sqrt {12-8}$
$\sqrt 4=\sqrt 4$ which is correct.
Work Step by Step
$\sqrt {\frac{p}{2}-2}=\sqrt {p-8}$
Square each side of the equation to get
$(\sqrt {\frac{p}{2}-2})^{2}=(\sqrt {p-8})^{2}$
$\implies \frac{p}{2}-2=p-8$
Simplifying, we have
$-2+8=p-\frac{p}{2}$
Or $6=\frac{p}{2}$
$\implies p=6\times2=12$
Check:
$\sqrt {\frac{12}{2}-2}=\sqrt {12-8}$
$\sqrt 4=\sqrt 4$ which is correct.
