Question

The gravitational force formula is F=Gm1m2 where F is the force between two objects, G is the constant of gravitation, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance between the objects. By rewriting the formula as r=√Gm1m2/F, you can find the distance between objects. Which of the following gives the distance, r, in simplest form?
the options are shown in the photo i attached

Answer 1

Answer: B.) r=((sqrtGm1m2F))/(F)

Step-by-step explanation:

Answer 2

$\text{r = }\dfrac{\sqrt{G*m_1*m_2}}{\sqrt{F}}$

This is what is in the middle of the second paragraph. That statement is correct.

I don't know that it is any simpler or not, but what they have done in the answer is rationalize the denominator. That means that the denominator is no longer under the square root sign.

To get that result, you multiply numerator and denominator by √F

When you do that, your get

$\text{r =}\dfrac{G\sqrt{m_1*m_2}\sqrt{F}} { \sqrt{F*}\sqrt{ F}}$

This results in the middle answer.

$\text{r = } \dfrac{ \sqrt{G m_1*m_2*F}}{F}$