## Intermediate Algebra (12th Edition)

$p=\pm5\sqrt{2}$
$\bf{\text{Solution Outline:}}$ 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}