Solve r^2=9*10^4*0.4*10^-6*0.8*10^-6/0.2

$$r ^ { 2 } = \frac { 9 \times 10 ^ { 4 } \times 0.4 \times 10 ^ { - 6 } \times 0.8 \times 10 ^ { - 6 } } { 0.2 }$$

Solve for r

$$r=\frac{3\sqrt{10}}{25000}\approx 0.000379473$$

$$r=-\frac{3\sqrt{10}}{25000}\approx -0.000379473$$

Steps by Finding Square Root

To multiply powers of the same base, add their exponents. Add 4 and -6 to get -2.

$$r^{2}=\frac{9\times 10^{-2}\times 0.4\times 0.8\times 10^{-6}}{0.2}$$

To multiply powers of the same base, add their exponents. Add -2 and -6 to get -8.

$$r^{2}=\frac{9\times 10^{-8}\times 0.4\times 0.8}{0.2}$$

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$r^{2}=\frac{9\times \frac{1}{100000000}\times 0.4\times 0.8}{0.2}$$

Multiply 9 and \frac{1}{100000000} to get \frac{9}{100000000}.

$$r^{2}=\frac{\frac{9}{100000000}\times 0.4\times 0.8}{0.2}$$

Multiply \frac{9}{100000000} and 0.4 to get \frac{9}{250000000}.

$$r^{2}=\frac{\frac{9}{250000000}\times 0.8}{0.2}$$

Multiply \frac{9}{250000000} and 0.8 to get \frac{9}{312500000}.

$$r^{2}=\frac{\frac{9}{312500000}}{0.2}$$

Express \frac{\frac{9}{312500000}}{0.2} as a single fraction.

$$r^{2}=\frac{9}{312500000\times 0.2}$$

Multiply 312500000 and 0.2 to get 62500000.

$$r^{2}=\frac{9}{62500000}$$

Take the square root of both sides of the equation.

$$r=\frac{3\sqrt{10}}{25000} r=-\frac{3\sqrt{10}}{25000}$$

Steps Using the Quadratic Formula

To multiply powers of the same base, add their exponents. Add 4 and -6 to get -2.

$$r^{2}=\frac{9\times 10^{-2}\times 0.4\times 0.8\times 10^{-6}}{0.2}$$

To multiply powers of the same base, add their exponents. Add -2 and -6 to get -8.

$$r^{2}=\frac{9\times 10^{-8}\times 0.4\times 0.8}{0.2}$$

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$r^{2}=\frac{9\times \frac{1}{100000000}\times 0.4\times 0.8}{0.2}$$

Multiply 9 and \frac{1}{100000000} to get \frac{9}{100000000}.

$$r^{2}=\frac{\frac{9}{100000000}\times 0.4\times 0.8}{0.2}$$

Multiply \frac{9}{100000000} and 0.4 to get \frac{9}{250000000}.

$$r^{2}=\frac{\frac{9}{250000000}\times 0.8}{0.2}$$

Multiply \frac{9}{250000000} and 0.8 to get \frac{9}{312500000}.

$$r^{2}=\frac{\frac{9}{312500000}}{0.2}$$

Express \frac{\frac{9}{312500000}}{0.2} as a single fraction.

$$r^{2}=\frac{9}{312500000\times 0.2}$$

Multiply 312500000 and 0.2 to get 62500000.

$$r^{2}=\frac{9}{62500000}$$

Subtract \frac{9}{62500000} from both sides.

$$r^{2}-\frac{9}{62500000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{62500000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{62500000}\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-\frac{9}{62500000}\right)}}{2}$$

Multiply -4 times -\frac{9}{62500000}.

$$r=\frac{0±\sqrt{\frac{9}{15625000}}}{2}$$

Take the square root of \frac{9}{15625000}.

$$r=\frac{0±\frac{3\sqrt{10}}{12500}}{2}$$

Now solve the equation r=\frac{0±\frac{3\sqrt{10}}{12500}}{2} when ± is plus.

$$r=\frac{3\sqrt{10}}{25000}$$

Now solve the equation r=\frac{0±\frac{3\sqrt{10}}{12500}}{2} when ± is minus.

$$r=-\frac{3\sqrt{10}}{25000}$$

The equation is now solved.

$$r=\frac{3\sqrt{10}}{25000} r=-\frac{3\sqrt{10}}{25000}$$