Solve y^2=1/16

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

Solve for y

$$y=\frac{1}{4}=0.25$$

$$y=-\frac{1}{4}=-0.25$$

Steps Using Difference of Squares

Subtract \frac{1}{16} from both sides.

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

Multiply both sides by 16.

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

Consider 16y^{2}-1. Rewrite 16y^{2}-1 as \left(4y\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4y-1\right)\left(4y+1\right)=0$$

To find equation solutions, solve 4y-1=0 and 4y+1=0.

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

Steps by Finding Square Root

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract \frac{1}{16} from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{16} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{16}\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{1}{16}\right)}}{2}$$

Multiply -4 times -\frac{1}{16}.

$$y=\frac{0±\sqrt{\frac{1}{4}}}{2}$$

Take the square root of \frac{1}{4}.

$$y=\frac{0±\frac{1}{2}}{2}$$

Now solve the equation y=\frac{0±\frac{1}{2}}{2} when ± is plus.

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

Now solve the equation y=\frac{0±\frac{1}{2}}{2} when ± is minus.

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

The equation is now solved.

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