Solve y^2=144*10^-5

$$y ^ { 2 } = 144 \times 10 ^ { - 5 }$$

Solve for y

$$y=\frac{3\sqrt{10}}{250}\approx 0.037947332$$

$$y=-\frac{3\sqrt{10}}{250}\approx -0.037947332$$

Steps by Finding Square Root

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$y^{2}=144\times \frac{1}{100000}$$

Multiply 144 and \frac{1}{100000} to get \frac{9}{6250}.

$$y^{2}=\frac{9}{6250}$$

Take the square root of both sides of the equation.

$$y=\frac{3\sqrt{10}}{250} y=-\frac{3\sqrt{10}}{250}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$y^{2}=144\times \frac{1}{100000}$$

Multiply 144 and \frac{1}{100000} to get \frac{9}{6250}.

$$y^{2}=\frac{9}{6250}$$

Subtract \frac{9}{6250} from both sides.

$$y^{2}-\frac{9}{6250}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{6250} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{6250}\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{9}{6250}\right)}}{2}$$

Multiply -4 times -\frac{9}{6250}.

$$y=\frac{0±\sqrt{\frac{18}{3125}}}{2}$$

Take the square root of \frac{18}{3125}.

$$y=\frac{0±\frac{3\sqrt{10}}{125}}{2}$$

Now solve the equation y=\frac{0±\frac{3\sqrt{10}}{125}}{2} when ± is plus.

$$y=\frac{3\sqrt{10}}{250}$$

Now solve the equation y=\frac{0±\frac{3\sqrt{10}}{125}}{2} when ± is minus.

$$y=-\frac{3\sqrt{10}}{250}$$

The equation is now solved.

$$y=\frac{3\sqrt{10}}{250} y=-\frac{3\sqrt{10}}{250}$$