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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 230. (page 1236)

In the following exercises, solve using the Square Root Property.
${(y - \frac{2}{3})}^{2} = \frac{2}{9}$

Short Answer

Expert verified

The required answer is $y = \frac{2}{3} + \frac{\sqrt{2}}{3} and y = \frac{2}{3} - \frac{\sqrt{2}}{3}$ .

Step by step solution

01

Step 1. Given information.

The given quadratic equation is:

${(y - \frac{2}{3})}^{2} = \frac{2}{9}$

02

Step 2. Solve using the quadratic equation by using Square Root Property.

{(y - \frac{2}{3})}^{2} = \frac{2}{9}

Use Square Root Property,

$y - \frac{2}{3} = 卤 \sqrt{\frac{2}{9}}$

Simplify the radical,

$y - \frac{2}{3} = 卤 \frac{\sqrt{2}}{\sqrt{9}} y - \frac{2}{3} = 卤 \frac{\sqrt{2}}{3}$

Write as two equations and solve,

$y - \frac{2}{3} = \frac{\sqrt{2}}{3} and y - \frac{2}{3} = - \frac{\sqrt{2}}{3} y = \frac{2}{3} + \frac{\sqrt{2}}{3} and y = \frac{2}{3} - \frac{\sqrt{2}}{3}$

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