Solve (v-8)^2-8=0

$$( v - 8 ) ^ { 2 } - 8 = 0$$

Solve for v

$$v=2\sqrt{2}+8\approx 10.828427125$$

$$v=8-2\sqrt{2}\approx 5.171572875$$

Steps by Finding Square Root

Add 8 to both sides of the equation.

$$\left(v-8\right)^{2}-8+8=8$$

Subtracting 8 from itself leaves 0.

$$\left(v-8\right)^{2}=8$$

Take the square root of both sides of the equation.

$$v-8=2\sqrt{2} v-8=-2\sqrt{2}$$

Add 8 to both sides of the equation.

$$v-8-\left(-8\right)=2\sqrt{2}-\left(-8\right) v-8-\left(-8\right)=-2\sqrt{2}-\left(-8\right)$$

Subtracting -8 from itself leaves 0.

$$v=2\sqrt{2}-\left(-8\right) v=-2\sqrt{2}-\left(-8\right)$$

Subtract -8 from 2\sqrt{2}.

$$v=2\sqrt{2}+8$$

Subtract -8 from -2\sqrt{2}.

$$v=8-2\sqrt{2}$$

The equation is now solved.

$$v=2\sqrt{2}+8 v=8-2\sqrt{2}$$