Solve 5=y^2-8

$$5 = y ^ { 2 } - 8$$

Solve for y

$$y=\sqrt{13}\approx 3.605551275$$

$$y=-\sqrt{13}\approx -3.605551275$$

Steps by Finding Square Root

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

$$y^{2}-8=5$$

Add 8 to both sides.

$$y^{2}=5+8$$

Add 5 and 8 to get 13.

$$y^{2}=13$$

Take the square root of both sides of the equation.

$$y=\sqrt{13} y=-\sqrt{13}$$

Steps Using the Quadratic Formula

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

$$y^{2}-8=5$$

Subtract 5 from both sides.

$$y^{2}-8-5=0$$

Subtract 5 from -8 to get -13.

$$y^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-13\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-13\right)}}{2}$$

Multiply -4 times -13.

$$y=\frac{0±\sqrt{52}}{2}$$

Take the square root of 52.

$$y=\frac{0±2\sqrt{13}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{13}}{2} when ± is plus.

$$y=\sqrt{13}$$

Now solve the equation y=\frac{0±2\sqrt{13}}{2} when ± is minus.

$$y=-\sqrt{13}$$

The equation is now solved.

$$y=\sqrt{13} y=-\sqrt{13}$$