Simplify assume all variables represent a positive real number

Question

(20+√75m^5)/15

Answer 1

So we have:

 

20+√(75m⁵)

      15

 

Let's look at √(75m⁵)

 

√(75m5) = √75√m⁵

 

√75 = √(25*3) = √25√3 = 5√3

 

√m⁵ = √(m⁴*m) = √m⁴ √m = m²√m

 

So if we look at the numerator as a whole now we get the following:

 

20+√(75m⁵) = 20+5m²√(3m) = 5(4+m²√(3m))

 

Putting this into our original equation we get 

 

20+√(75m⁵)     = 5(4+m²√(3m))  = 4+m²√(3m)
      15                         15                       3

 

I do believe that is about as simplified as you can get it without any additional information. 

 

Hope this helps!