Solve 1=y^2*1/sqrt{256}

$$1= { y }^{ 2 } \times \frac{ 1 }{ \sqrt{ 256 } }$$

Solve for y

$$y=4$$

$$y=-4$$

Steps Using Difference of Squares

Calculate the square root of 256 and get 16.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract 1 from both sides.

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

Multiply both sides by 16.

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

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

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

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

$$y=4 y=-4$$

Steps by Finding Square Root

Calculate the square root of 256 and get 16.

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

Swap sides so that all variable terms are on the left hand side.

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

Multiply both sides by 16, the reciprocal of \frac{1}{16}.

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

Multiply 1 and 16 to get 16.

$$y^{2}=16$$

Take the square root of both sides of the equation.

$$y=4 y=-4$$

Steps Using the Quadratic Formula

Calculate the square root of 256 and get 16.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract 1 from both sides.

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

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

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

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

Square 0.

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

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

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

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

$$y=\frac{0±\sqrt{\frac{1}{4}}}{2\times \frac{1}{16}}$$

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

$$y=\frac{0±\frac{1}{2}}{2\times \frac{1}{16}}$$

Multiply 2 times \frac{1}{16}.

$$y=\frac{0±\frac{1}{2}}{\frac{1}{8}}$$

Now solve the equation y=\frac{0±\frac{1}{2}}{\frac{1}{8}} when ± is plus.

$$y=4$$

Now solve the equation y=\frac{0±\frac{1}{2}}{\frac{1}{8}} when ± is minus.

$$y=-4$$

The equation is now solved.

$$y=4 y=-4$$