Solve 8y^2=40

$$8 y ^ { 2 } = 40$$

Solve for y

$$y=\sqrt{5}\approx 2.236067977$$

$$y=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Divide both sides by 8.

$$y^{2}=\frac{40}{8}$$

Divide 40 by 8 to get 5.

$$y^{2}=5$$

Take the square root of both sides of the equation.

$$y=\sqrt{5} y=-\sqrt{5}$$

Steps Using the Quadratic Formula

Divide both sides by 8.

$$y^{2}=\frac{40}{8}$$

Divide 40 by 8 to get 5.

$$y^{2}=5$$

Subtract 5 from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-5\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-5\right)}}{2}$$

Multiply -4 times -5.

$$y=\frac{0±\sqrt{20}}{2}$$

Take the square root of 20.

$$y=\frac{0±2\sqrt{5}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{5}}{2} when ± is plus.

$$y=\sqrt{5}$$

Now solve the equation y=\frac{0±2\sqrt{5}}{2} when ± is minus.

$$y=-\sqrt{5}$$

The equation is now solved.

$$y=\sqrt{5} y=-\sqrt{5}$$