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24/sqr3

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by Tega1984 » Mon May 16, 2011 4:55 am
Here's the link for a question that I got doing the 800score quant test.

https://www.800score.com/explanations/GM ... T1_Q1.html

Can anyone tell me how does 24/square root of3=(24 square root of3)/3? That's mentioned in step 6.
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by MAAJ » Mon May 16, 2011 5:58 am
PS: I sent you a PM!!!

We can simplify expresions like this if we multiply the numerator and denominator by the same root (in this case sqrt(3)). The value won't be changed because its the same as multiplying by 1. It's just to change the "format" of the fraction to make it simplier to read.

[24/sqrt(3)] * [sqrt(3)/sqrt(3)]
[24*sqrt(3)]/[sqrt(3)^2]
[24*sqrt(3)]/3
8*sqrt(3)

Tega1984 wrote:Here's the link for a question that I got doing the 800score quant test.

https://www.800score.com/explanations/GM ... T1_Q1.html

Can anyone tell me how does 24/square root of3=(24 square root of3)/3? That's mentioned in step 6.
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by Stuart@KaplanGMAT » Mon May 16, 2011 8:53 am
MAAJ wrote:PS: I sent you a PM!!!

We can simplify expresions like this if we multiply the numerator and denominator by the same root (in this case sqrt(3)). The value won't be changed because its the same as multiplying by 1. It's just to change the "format" of the fraction to make it simplier to read.

[24/sqrt(3)] * [sqrt(3)/sqrt(3)]
[24*sqrt(3)]/[sqrt(3)^2]
[24*sqrt(3)]/3
8*sqrt(3)
Great explanation!

To go one step further, what Maaj did is called "rationalizing the denominator"; it's considered bad form in math to leave an irrational number (e.g. a root) in the bottom of a fraction.

Accordingly, on the GMAT you'll almost never see a root in the denominator of a fraction. To eliminate it, simply follow Maaj's recommendation and multiply both the top and the bottom of the fraction by the root that's already in the denominator.
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by Tega1984 » Mon May 16, 2011 9:01 am
Yeah you're right, I forgot that and know I recalled:)
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