Working through the MGMAT Equations, Inequalities
, and VICs book and encounter a roots answer in chapter 4 that totally stumps me. The specific question is #9 on page 63.
You have to pick numbers for the question and end up with a fraction as follows: √1/2, (whole fraction under radical) which then becomes 1/√2 = √2/2 (only numerator under radical) -> wait what? what's the general property that I need to know here? Any square root with a numerator of 1 can just be rewritten by moving the radical to the denominator? And on top of that, how do you know to then make it √2/2 (only numerator under radical) ?? I guess I just havent seen this manipulation before and it just strikes me as hard to think through. It's not easy to see how they are equal.
On top of that, a further twist regarding the manipulation:
As you are working through the math you get to 2√3/√2 which is then manipulated as such: 2√3(√2)/2 ->huh? How did you move the sqrt of 2 from the bottom to the top (not only moving, but retaining it in the bottom as well)??
Any help would be greatly appreciated