Solve y^2=19

$$y ^ { 2 } = 19$$

Solve for y

$$y=\sqrt{19}\approx 4.358898944$$

$$y=-\sqrt{19}\approx -4.358898944$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$y=\sqrt{19} y=-\sqrt{19}$$

Steps Using the Quadratic Formula

Subtract 19 from both sides.

$$y^{2}-19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-19\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-19\right)}}{2}$$

Multiply -4 times -19.

$$y=\frac{0±\sqrt{76}}{2}$$

Take the square root of 76.

$$y=\frac{0±2\sqrt{19}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{19}}{2} when ± is plus.

$$y=\sqrt{19}$$

Now solve the equation y=\frac{0±2\sqrt{19}}{2} when ± is minus.

$$y=-\sqrt{19}$$

The equation is now solved.

$$y=\sqrt{19} y=-\sqrt{19}$$