2^(1/2)/4 + 3/(2*2^(1/2)) or \sqrt{2}\4 GMAT

2^(1/2)/4 + 3/(2*2^(1/2)) or \sqrt{2}\4

(The most difficult thing about this question is writing it in a way that will be found by the search engines–which don’t appreciate LaTeX code–so please forgive me having to write shit like 2^(1/2)/4 + 3/(2*2^(1/2)) or \sqrt{2}\4 over and over).

All that out of the way, the question itself isn’t really that bad. 

We have to add two fractions with different denominators. How does one do so? Find a common denominator, of course.

So the common denominator here might not be immediately obvious, but we do have one trick up our sleeves: one of the fractions has a root in the bottom, which means that we ultimately need to get this root off the bottom if we expect the fraction to work. 

The way to do this is our old friend: Rationalizing the Denominator. 

WE don’t need to get into the “whys” of where Rationalizing comes from, but suffice it to say that it’s thoroughly pointless and a holdover from some long-dead Math Karen. It’s still in the GMAT curriculum, however, so it’s your responsibility to know this.

Basically, find the root–in this case –and multiply the fraction in question by 1 phrased as . This will blow open the root on the bottom. 

1. What we need to do is make the denominators the same, but the first step is to get the root off the bottom of the second one.

Check this out (looking at the second fraction):

After using this process to reduce the second fraction, we can now add it to the first one:

You’ll notice that that’s one on the left and 3 s on the right. It’s as simple as to say :

The answer is C.

I’m going to write a bunch of shit like \frac{\sqrt{2}}{4} and 2^(1/2)/4 + 3/(2*2^(1/2)) again just for SEO. I hate SEO. Sorry.