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24 Aug 2010, 10:36
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Hello all,
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
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
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24 Aug 2010, 14:17
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Hi HustleHarder,
One property of fraction is that the fraction remains same if you multiply or divide the numerator and denominator with the same value.
In √1/2, (whole fraction under radical) we can write it as √1/√2 ( another property of square rt. √(X/Y) = √X/√Y
now we know that √1 = 1 so the complete fraction turns out to 1/√2.
if we multiply both numerator and denominator by √2, we get √2/(√2 * √2)
here we have to apply another property of sq rt. √X*√Y = √(X*Y)
so the fraction becomes √2/√(2*2) = √2/√4 = √2/2 (since √4 = 2).
regarding, 2√3/√2 here we are multiplying both the numerator and denominator by the same value √2 so we get 2√3√2/√2√2 = 2√3√2 / √(2*2) = 2√3√2/ √4 = 2√3√2/2 = √6
-Please let me know if you need more description in any of these [:)]
One property of fraction is that the fraction remains same if you multiply or divide the numerator and denominator with the same value.
In √1/2, (whole fraction under radical) we can write it as √1/√2 ( another property of square rt. √(X/Y) = √X/√Y
now we know that √1 = 1 so the complete fraction turns out to 1/√2.
if we multiply both numerator and denominator by √2, we get √2/(√2 * √2)
here we have to apply another property of sq rt. √X*√Y = √(X*Y)
so the fraction becomes √2/√(2*2) = √2/√4 = √2/2 (since √4 = 2).
regarding, 2√3/√2 here we are multiplying both the numerator and denominator by the same value √2 so we get 2√3√2/√2√2 = 2√3√2 / √(2*2) = 2√3√2/ √4 = 2√3√2/2 = √6
-Please let me know if you need more description in any of these [:)]
24 Aug 2010, 15:27
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Dude. Do you know you are the man? Thanks!!! Makes total sense now. Had the eureka moment. I may have some more soon...
