# How do you solve 9y² = 16?

Mar 28, 2016

$y = \frac{4}{3}$

#### Explanation:

color(blue)(9y^2=16

Divide both sides by $9$

$\rightarrow \frac{\cancel{9} {y}^{2}}{\cancel{9}} = \frac{16}{9}$

$\rightarrow {y}^{2} = \frac{16}{9}$

Take the square root of both sides

$\rightarrow \sqrt{{y}^{2}} = \sqrt{\frac{16}{9}}$

$\rightarrow y = \sqrt{\frac{16}{9}}$

Remember that color(brown)(sqrt(a/b)=sqrta/sqrtb

$\therefore \sqrt{\frac{16}{9}} = \frac{\sqrt{16}}{\sqrt{9}}$

$\rightarrow y = \frac{\sqrt{16}}{\sqrt{9}}$

color(green)(rArry=4/3=1.bar9

Remember that the $\overline{9}$ means it is repeating...

Eg.$3.555555555 . .$ can be written as $3. \overline{5}$

$\therefore \frac{4}{3} = 1.999999999 . .$ is written as $1. \overline{9}$