A homeowner decides to install a solar home-heating system. The company selling the system offers her two options: Option A costs $20,000 to install plus an additional annual heating cost of $1000; Option B costs $15,000 to install plus an additional annual heating cost of $1500.

C.
Factor 550 into its prime factors
           550 = 2 • 52 • 11 

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :
           25 = 52 

Factors which will remain inside the root are :
           22 = 2 • 11 

To complete the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
           5 = 5 

The simplified SQRT looks like this: 
         5 • sqrt (22)