Answer
$r=\frac{\sqrt{Ap}}{p}-1$
Work Step by Step
To solve for r, isolate r on one side of the equation.
$A=p(1+r)^2$
Divide both sides by p.
$\frac{A}{p}=\frac{p(1+r)^2}{p}$
Simplify.
$\frac{A}{p}=(1+r)^2$
Take the square root of each side.
$\sqrt{\frac{A}{p}}=\sqrt{(1+r)^2}$
Simplify.
$\sqrt{\frac{A}{p}}=1+r$
Subtract 1 from each side.
$\sqrt{\frac{A}{p}}-1=1+r-1$
Simplify.
$\sqrt{\frac{A}{p}}-1=r$
Rationalize the denominator.
$r=\sqrt{\frac{A}{p}}-1=\frac{\sqrt A}{\sqrt p}-1=\frac{\sqrt A\times \sqrt p}{\sqrt p\times\sqrt p}-1=\frac{\sqrt{Ap}}{p}-1$
