Question

Solve the quadratic equation using square root property.

$(y-4{)}^2=64$

Short answer

The solutions are$y=-4,12$.

Step-by-step solution

Given Information.  

The Given equation is$(y-4{)}^2=64$.

Use square root property. 

$y-4=\pm \sqrt{64}$

Factor and solve radical.

$$\begin{gathered} y-4=\pm \sqrt{8\times 8} \\ y-4=\pm 8 \end{gathered}$$

Solve for  y.

$$\begin{gathered} y-4=\pm 8 \\ y=4\pm 8 \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} y=4+8=12 \\ y=4-8=-4 \end{gathered}$$

Thus, the solutions are$y=-4,12$.