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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 37 (page 1165)

Solve the quadratic equation using square root property.
$a^{2} - 18 = 0$

Short Answer

Expert verified

The solutions are $a = 卤 3 \sqrt{2}$ .

Step by step solution

01

Given Information

The Given equation is $a^{2} - 18 = 0$ .

02

Isolate the quadratic term and makes its coefficient one.

$a^{2} - 18 = 0 a^{2} = 18$

03

Use the square root property.

$a = 卤 \sqrt{18}$

Factor the radicand.

$a = 卤 \sqrt{2 脳 3 脳 3} a = 卤 3 \sqrt{2}$

04

Check the solutions.

Substitute $a = 3 \sqrt{2}$

$a^{2} - 18 = 0 {(3 \sqrt{2})}^{2} - 18 \overset{?}{=} 0 18 - 18 \overset{?}{=} 0 0 = 0 T r u e$

Substitute $a = - 3 \sqrt{2}$

$a^{2} - 18 = 0 {(- 3 \sqrt{2})}^{2} - 18 \overset{?}{=} 0 18 - 18 \overset{?}{=} 0 0 = 0$

Thus, the solutions are $a = 卤 3 \sqrt{2}$

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