Question

Solve Quadratic Equations Using the Square Root Property :${\left(y-\frac{2}{3}\right)}^2=\frac{2}{9}$

Short answer

The required result is$y=\frac{\sqrt{2}+2}{3},\frac{-\sqrt{2}+2}{3}$

Step-by-step solution

Given information  .  

The given expression is${\left(y-\frac{2}{3}\right)}^2=\frac{2}{9}$

Use square root property   

$$\begin{gathered} {\left(y-\frac{2}{3}\right)}^2=\frac{2}{9} \\ \left(y-\frac{2}{3}\right)=\pm \sqrt{\frac{2}{9}} \\ \left(y-\frac{2}{3}\right)=\pm \frac{\sqrt{2}}{3} \\ y=\pm \frac{\sqrt{2}}{3}+\frac{2}{3} \\ y=\frac{\sqrt{2}+2}{3},\frac{-\sqrt{2}+2}{3} \end{gathered}$$