Solve for y y^2-1/16=0

$y^{2} - \frac{1}{16} = 0$

Step 1

Add $\frac{1}{16}$ to both sides of the equation.

$y^{2} = \frac{1}{16}$

Step 2

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{\frac{1}{16}}$

Step 3

Simplify $\pm \sqrt{\frac{1}{16}}$ .

Rewrite $\sqrt{\frac{1}{16}}$ as $\frac{\sqrt{1}}{\sqrt{16}}$ .

$y = \pm \frac{\sqrt{1}}{\sqrt{16}}$

Any root of $1$ is $1$ .

$y = \pm \frac{1}{\sqrt{16}}$

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$y = \pm \frac{1}{\sqrt{4^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm \frac{1}{4}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \frac{1}{4}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \frac{1}{4}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{1}{4}, - \frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1}{4}, - \frac{1}{4}$

Decimal Form:

$y = 0.25, - 0.25$