Solve (y-3)^2-24=0

$$( y - 3 ) ^ { 2 } - 24 = 0$$

Solve for y

$$y=2\sqrt{6}+3\approx 7.898979486$$

$$y=3-2\sqrt{6}\approx -1.898979486$$

Steps by Finding Square Root

Add 24 to both sides of the equation.

$$\left(y-3\right)^{2}-24+24=24$$

Subtracting 24 from itself leaves 0.

$$\left(y-3\right)^{2}=24$$

Take the square root of both sides of the equation.

$$y-3=2\sqrt{6} y-3=-2\sqrt{6}$$

Add 3 to both sides of the equation.

$$y-3-\left(-3\right)=2\sqrt{6}-\left(-3\right) y-3-\left(-3\right)=-2\sqrt{6}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$y=2\sqrt{6}-\left(-3\right) y=-2\sqrt{6}-\left(-3\right)$$

Subtract -3 from 2\sqrt{6}.

$$y=2\sqrt{6}+3$$

Subtract -3 from -2\sqrt{6}.

$$y=3-2\sqrt{6}$$

The equation is now solved.

$$y=2\sqrt{6}+3 y=3-2\sqrt{6}$$