24/sqr3

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Tega1984: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Wed Oct 13, 2010 4:47 am; Thanked: 2 times; GMAT Score:560

24/sqr3

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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Source: Beat The GMAT — Problem Solving | Mon May 16, 2011 4:55 am

MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 am; Location: Dominican Republic; Thanked: 31 times; Followed by:2 members; GMAT Score:480

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.

"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

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.