Q. 29 - Intermediate Algebra

Question

In the following exercises, solve each equation.

${\left(y+\frac{2}{3}\right)}^2=\frac{8}{81}$

Step-by-Step Solution

Answer

The solution of the equation is $y=\frac{-6+2\sqrt{2}}{9},\frac{-6-2\sqrt{2}}{9}$

Step 1. Given information

In the given question we have to solve given equation. 

${\left(y+\frac{2}{3}\right)}^2=\frac{8}{81}$

Step 2. The given equation is y + 2 3 2 = 8 81

Use the Square Root Property.

$y+\frac{2}{3}=\pm \sqrt{\frac{8}{81}}$

$y+\frac{2}{3}=\pm \frac{\sqrt{8}}{\sqrt{81}}$

Step 3. Simplify the radical.

$y+\frac{2}{3}=\pm \frac{2\sqrt{2}}{9}$

Subtract $\frac{2}{3}$on both side

$$\begin{gathered} y+\frac{2}{3}-\frac{2}{3}=-\frac{2}{3}\pm \frac{2\sqrt{2}}{9} \\ y=-\frac{2}{3}\pm \frac{2\sqrt{2}}{9} \end{gathered}$$

Step 4. Solve for y

$$\begin{gathered} y=-\frac{2}{3}+\frac{2\sqrt{2}}{9} y=-\frac{2}{3}-\frac{2\sqrt{2}}{9} \\ y=\frac{-6+2\sqrt{2}}{9} y=\frac{-6-2\sqrt{2}}{9} \end{gathered}$$