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Square Roots Question
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24 Aug 2010, 10:36
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
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Re: Square Roots Question
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24 Aug 2010, 14:17
1
Kudos
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 [:)]
Re: Square Roots Question
[#permalink]
24 Aug 2010, 20:56
Got another one here, this time compound functions where you have to find a value of x for which f(g(x)) = g(f(x)) given that f(x) = x^3 + 1 and g(x) = 2x. I set it up as follows:
f(2x) = g(x^3+1) now this is where the MGMAT book does another quantum leap in algebraic manipulation that leaves me dumbfounded. It takes the expression above and turns it to:
(2x)^3+1 = 2(x^3+1)
wuh wuh whaaa? They do not explain what they are doing to manipulate the equation. Help would be appreciated again : )
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