Stellar Radius & Effective Temperature

[Physics Dad]

I have a question for my Astro homework and I am a little unsure as to whether I am going in the right direction

Question
Using an expression that relates luminosity, size and temperature of a star, and assuming all Main Sequence stars have the same mean density, determine the relationship between stellar radius and effective temperature.

Relevant equations
L=4πR²σT⁴
L∝M^3.5

Attempt at a solution
My thinking is to use the solar version of the above equation and this one, dividing one by the other to get rid of the 4π and σ and making...

R=R_Θ(√(L/L_Θ))(T_effΘ/T_eff)²

However I don't know if I am supposed to just have R and T with no other variable.

Any guidance would be appreciated.

 

[haruspex]

My thinking is to use the solar version of the above equation and this one, dividing one by the other

I don't think that is the right line. The information regarding density implies you are supposed to use some fact concerning mass to eliminate luminosity. Your second Relevant Equation looks useful in that regard.