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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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Most popular questions from this chapter

The sun casts a shadow from a flag pole. The height of the flag pole is three times the length of its shadow. The distance between the end of the shadow and the top of the flag pole is 20 feet. Find the length of the shadow and the length of the flag pole. Round to the nearest tenth.

Solve the equation $y^{2} + 8 y = 48$ by completing the square and explain all your steps.

The product of two consecutive even integers is 168. Find the integers.

Solve by using the quadratic formula.

$\frac{2}{5} q^{2} + \frac{3}{10} q = \frac{1}{10}$

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