Solve r^2=5000/3.14

$$r ^ { 2 } = \frac { 5000 } { 3.14 }$$

Solve for r

$$r = \frac{500 \sqrt{157}}{157} \approx 39.904344223$$

$$r = -\frac{500 \sqrt{157}}{157} \approx -39.904344223$$

Steps by Finding Square Root

Expand \frac{5000}{3.14} by multiplying both numerator and the denominator by 100.

$$r^{2}=\frac{500000}{314}$$

Reduce the fraction \frac{500000}{314} to lowest terms by extracting and canceling out 2.

$$r^{2}=\frac{250000}{157}$$

Take the square root of both sides of the equation.

$$r=\frac{500\sqrt{157}}{157} r=-\frac{500\sqrt{157}}{157}$$

Steps Using the Quadratic Formula

Expand \frac{5000}{3.14} by multiplying both numerator and the denominator by 100.

$$r^{2}=\frac{500000}{314}$$

Reduce the fraction \frac{500000}{314} to lowest terms by extracting and canceling out 2.

$$r^{2}=\frac{250000}{157}$$

Subtract \frac{250000}{157} from both sides.

$$r^{2}-\frac{250000}{157}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{250000}{157} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{250000}{157}\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-\frac{250000}{157}\right)}}{2}$$

Multiply -4 times -\frac{250000}{157}.

$$r=\frac{0±\sqrt{\frac{1000000}{157}}}{2}$$

Take the square root of \frac{1000000}{157}.

$$r=\frac{0±\frac{1000\sqrt{157}}{157}}{2}$$

Now solve the equation r=\frac{0±\frac{1000\sqrt{157}}{157}}{2} when ± is plus.

$$r=\frac{500\sqrt{157}}{157}$$

Now solve the equation r=\frac{0±\frac{1000\sqrt{157}}{157}}{2} when ± is minus.

$$r=-\frac{500\sqrt{157}}{157}$$

The equation is now solved.

$$r=\frac{500\sqrt{157}}{157} r=-\frac{500\sqrt{157}}{157}$$