Hi All,

In the following question

The competitive edge of a baseball team is defined as $\displaystyle \sqrt{\frac{W}{L}} $. W = number of wins, L = number of losses. This year a the team had 3 times as many wins and $\displaystyle \frac{1}{2} $ as many losses. By what factor did the competitive edge increase?

1. $\displaystyle c = \sqrt{\frac{W}{L}} $ where c = competitive edge.

2. Need to determine the original competitive edge so pick numbers $\displaystyle c = \sqrt{\frac{2}{4}} $

3. Simplify $\displaystyle c = \sqrt{\frac{2}{4}} $ = $\displaystyle c = \sqrt{\frac{1}{2}} $ = $\displaystyle c = \frac{\sqrt{1}}{\sqrt{2}} $ = $\displaystyle c = \frac{1}{\sqrt{2}} $

QUESTION ONE. I would typically stop the symplification here. However the question went on to state $\displaystyle c = \frac{\sqrt{2}}{2} $ I understand HOW this next step was derived. What I'm trying to understand is WHY (i.e how did the author know the process required this extra step)?

4. $\displaystyle W.3 $ $\displaystyle L.\frac{1}{2} $ = $\displaystyle c = \sqrt{\frac{6}{2}} = \sqrt{3}} $

5. $\displaystyle \frac{\sqrt{2}}{2}X = \sqrt{3}} $ = $\displaystyle \frac{\sqrt{3}}{1}.\frac{2}{\sqrt{2}} = \frac{2_\sqrt{3}}{\sqrt{2}} $

QUESTION TWO. I would stop sympifying here. However the question went on to state $\displaystyle \frac{2_\sqrt{3}\sqrt{2}}{\sqrt{2}\sqrt{2}} $ $\displaystyle X = \sqrt{3}\sqrt{2} $. Again I understand the HOW. What I'm tring to understand is WHY (i.e. how did the author know to simplify it further)?

I hope that makes sense.

Thanks,

D