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Problem Solving - Roots question

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by MOARQUESTIONS » Wed Oct 19, 2011 1:41 pm
I didn't understand the answer to this question. Hopefully one of you GMAT wizards can give me clarity on it.

Roots are kind of hard to illustrate on boards so I used arrows to space it.

3sqrt(3) -->4sqrt(3)
________ X ________

sqrt(2) --->3


A) 3
B) 6sqrt(2)
C) 12
D) 12sqrt(2)
E) 36

[spoiler]ANSWER : B[/spoiler]
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by neelgandham » Wed Oct 19, 2011 2:15 pm
Do you mind re-framing ? Never understood a bit !
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by GMATGuruNY » Wed Oct 19, 2011 2:37 pm
MOARQUESTIONS wrote:I didn't understand the answer to this question. Hopefully one of you GMAT wizards can give me clarity on it.

Roots are kind of hard to illustrate on boards so I used arrows to space it.

3sqrt(3) -->4sqrt(3)
________ X ________

sqrt(2) --->3


A) 3
B) 6sqrt(2)
C) 12
D) 12sqrt(2)
E) 36

[spoiler]ANSWER : B[/spoiler]
Combining the two fractions into one, we get:

= (3√3)(4√3) / (√2)*3 -- Divide each side by 3.

= 4 * (√3)(√3) / (√2) -- Multiply (√3)(√3)=3.

=4*3 / √2 -- Multiply 4*3.

=12 * √2 / (√2*√2) -- To eliminate √2 from the denominator, multiply by √2/√2.

= 12√2 / 2 -- Divide by 2.

= 6√2.

The correct answer is B.
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by MOARQUESTIONS » Wed Oct 19, 2011 2:37 pm
Just got home from the library, decided it was tablet time. :)
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by MOARQUESTIONS » Fri Oct 21, 2011 12:57 pm
Thanks for the answer, however I just don't understand the first step. I understand how you simplified the subsequent parts, but if you could explain in another way why you divided each side by three and how you got from that to the 2nd step that would be great.
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by Anurag@Gurome » Fri Oct 21, 2011 9:45 pm
MOARQUESTIONS wrote:I understand how you simplified the subsequent parts, but if you could explain in another way why you divided each side by three and how you got from that to the 2nd step that would be great.
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by MOARQUESTIONS » Sat Oct 22, 2011 12:46 pm
Thanks! That was a perfectly illustrated answer!
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by TrueGritMick » Sat Oct 22, 2011 1:24 pm
My key to looking at this question was basic properties of fractions - to multiply two fractions, you just multiply numerator with numerator and denominator with denominator, straight across.

From there, its just properties of radicals and simplifying the fraction.

Thanks MOAR and Anurag for posting and answering this question!
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