Convention for Fractions with Radicals!

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kdn508: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Fri Nov 15, 2013 4:10 pm; Location: San Diego

by kdn508 » Wed Mar 12, 2014 5:08 pm

Hello All, so I'm currently working in the MGMAT Quant Foundations book! I'm currently reviewing fractions and radicals and I came across this problem.

(sqrt(25)/sqrt(10)) *(sqrt(8)/sqrt(15) =

I was able to break numbers into primes really quick and cancel out, but when I checked my answer in the book they left Sqrt(3) in the denominator

book answer (2/sqrt(3))

What I did (2/sqrt(3)) * sqrt(3) = ((2*sqrt(3))/3)

What is the proper convention? I thought you should never have a radical in the denominator?

Source: Beat The GMAT — Problem Solving | Wed Mar 12, 2014 5:08 pm

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Wed Mar 12, 2014 8:14 pm

You are right about the convention, but "never" is too strong. Your answer is mathematically equivalent to the book's answer so your answer is right. On the test, let the answer choices guide you. Most of the time you will need to get rid of the root in the denominator, but not necessarily every time.

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by [email protected] » Wed Mar 12, 2014 11:14 pm

Hi kdn508,

As a general rule, radicals in the denominator are "frowned upon", so your "math move" would be required. Patrick does bring up a fair point though - be prepared to adjust your answer to what the answer choices give you to work with. Sometimes you'll have to convert fractions to decimals (and vice versa) or convert units to other units (dollars to cents, minutes to seconds, etc.), so do enough work until the answers give you a reason to stop.

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by Bill@VeritasPrep » Thu Mar 13, 2014 8:30 am

A good example of why you should check the answers before you start solving. A radical in the denominator should stand out as a little weird.

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