# Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set: 66

$r=\frac{\sqrt{Ap}}{p}-1$

#### 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. $r=\sqrt{\frac{A}{p}}-1=\frac{\sqrt A}{\sqrt p}-1=\frac{\sqrt A\times \sqrt p}{\sqrt p\times\sqrt p}-1=\frac{\sqrt{Ap}}{p}-1$

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