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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.406. (page 982)

Solve using the square root property.
${(y - \frac{2}{3})}^{2} = \frac{2}{9}$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

The given equation is ${(y - \frac{2}{3})}^{2} = \frac{2}{9}$ .

02

Step 2. Apply the square root property.

The property states that $x^{2} = k$ , then $x = 卤 \sqrt{k}$ .

03

Step 3. Simplify the equation.

$\begin{array}{rcl} {(y - \frac{2}{3})}^{2} & = & \frac{2}{9} \\ y - \frac{2}{3} & = & 卤 \sqrt{\frac{2}{9}} \\ y - \frac{2}{3} & = & 卤 \frac{\sqrt{2}}{3} \\ y & = & 卤 \frac{\sqrt{2}}{3} + \frac{2}{3} \end{array}$

04

Step 4. Simplified answer.

Hence, the required solution is $\begin{array}{rcl} y & = & \frac{\sqrt{2}}{3} + \frac{2}{3} \end{array}$ and $\begin{array}{rcl} y & = & - \frac{\sqrt{2}}{3} + \frac{2}{3} \end{array}$ .

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