Lesson: “Fixing” the Denominator

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I think rather than using FOIL method, I'd use algebraic identity (a+b)(a-b) = a^2-b^2. It might save a second or two when dealing with conjugates.
gmat-admin's picture

I totally agree that that would save time.
I don't mention the Difference of Squares approach (found here https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...), because many students follow the course as it's laid out in the Learning Guide, and those students haven't covered that lesson yet.

For the second question, why aren't we multiplying 3 X root 25, which is 5, to get 2 root 50 in the numerator and 15 in the denominator? Thanks!
gmat-admin's picture

That's totally valid. However, once we get to (2√50)/15, we need to recognize that we can simplify this fraction further, since √50 = √(25 x 2) = √25 x √2 = 5√2

So, (2√50)/15 = 2(5√2)/15 = 2√2/3

Hi Brent,

What would be the conjugate of a denominator with 3 variables (e.g. 3+3√7-4√6)? Would that ever be asked?
gmat-admin's picture

Here's a video on rationalizing the denominator when there are 3 terms: https://www.youtube.com/watch?v=pPtOMrrsoME

As you can see, the technique is far too time consuming to ever be part of a GMAT test. So, don't worry about it.

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