Facing a Challenge

The first time I tried this problem I found it challenging because I tried to multiply both the denominator and numerator by √3, which would never rationalize the denominator because the (√3+1) would turn into (3+√3) and repeat the rationalization cycle anew. When this happened, I employed my favourite trick to solve problems: I stared blankly at the question as it sat on my workbook, hoping for a stray cosmic particle to collide with a brain cell and kick-start some Archimedes-tier revelation in my brain to give me the guidance I needed to solve this question. It didn’t work. I then employed my second favourite trick to solving problems: looking in the resources that you have given us. A cursory glance in the 1.6 (part 2) page in the OneNote reveals a shocking truth – should the denominator have more than 1 term, the procedure is to multiply both the numerator and denominator by the conjugate of the denominator. The one concept I needed to remember to solve this problem is the concept of seeking help when stuck on a problem. Truly, a trait like this is only present in 0.001% of the population. I can assure you that I will not try to solve my next math-related problem by staring blankly at it – I will actually be active in looking for a solution. Crazy, right?

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