## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 4 Quadratic Functions and Factoring - 4.5 Solve Quadratic Equations by Finding Square Roots - 4.5 Exercises - Skill Practice - Page 270: 26

#### Answer

The solutions are $4\sqrt{7}$ and $-4\sqrt{7}$

#### Work Step by Step

$4p^{2}=448\qquad$ ...divide each side with $4$ $p^{2}=112\qquad$ ...take square roots of each side. $\sqrt{p^{2}}=\sqrt{112}\qquad$ ...simplify ...When solving an equation of the form $x^{2}=s$ where $s>0$, we find both the positive and negative solutions. $p=\pm\sqrt{112}\qquad$ ...rewrite $112$ as a product of two factors so that one factor is a perfect square. ($112=16\cdot 7$) $p=\pm\sqrt{16\cdot 7}\qquad$ ...use the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ $p=\pm\sqrt{16}\cdot\sqrt{7}\qquad$ ...evaluate $\sqrt{16}$ ($\sqrt{16}=4$) $p=\pm 4\sqrt{7}$

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