Square Root of Variables

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bml1105: Master | Next Rank: 500 Posts; Posts: 113; Joined: Sun Nov 24, 2013 9:19 pmFollowed by: 5 members; Thanked: 1 times

by bml1105 » Sat Dec 21, 2013 6:24 pm

MGMAT - Algebra Guide Chapter 4: Roots, Problem Set #11

Solve of simplify the following problem:

âˆšx^2y^3 = 3x^2y^3

Answer = [spoiler]2xyâˆšy[/spoiler]

Why not [spoiler]2xâˆš2y^3[/spoiler]?

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Source: Beat The GMAT — Problem Solving | Sat Dec 21, 2013 6:24 pm

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

by Stuart@KaplanGMAT » Sat Dec 21, 2013 6:33 pm

bml1105 wrote:MGMAT - Algebra Guide Chapter 4: Roots, Problem Set #11

Solve of simplify the following problem:

âˆšx^2y^3 = 3x^2y^3

Answer = [spoiler]2xyâˆšy[/spoiler]

Why not [spoiler]2xâˆš2y^3[/spoiler]?

Hi!

First, the problem you posted doesn't actually include a question, so I'm not sure for what you're solving. In other words, you posted an equation, but no question.

However, I can still answer your question - the official answer you posted and your answer are actually identical.

We can rewrite 2xâˆš2y^3 as 2xâˆš2(y*y^2)

and then we can take "y^2" our of the root to get the accredited answer.

Looking at a simpler example:

âˆšy^3 = âˆšy^2*y = âˆšy^2 * âˆšy = yâˆšy

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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bml1105: Master | Next Rank: 500 Posts; Posts: 113; Joined: Sun Nov 24, 2013 9:19 pmFollowed by: 5 members; Thanked: 1 times

by bml1105 » Sat Dec 21, 2013 9:24 pm

Sorry, the question was just to solve or simplify. However, my equation wasn't clear and I accidentally put an equals sign where there should be a plus sign.

The equation I'm supposed to simplify is: âˆš[(x^2)(y^3) + (3x^2)(y^3)]

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

by Stuart@KaplanGMAT » Sun Dec 22, 2013 1:22 am

bml1105 wrote:Sorry, the question was just to solve or simplify. However, my equation wasn't clear and I accidentally put an equals sign where there should be a plus sign.

The equation I'm supposed to simplify is: âˆš[(x^2)(y^3) + (3x^2)(y^3)]

No worries! It didn't really affect your question or my response, I was just curious.

Stuart

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bml1105: Master | Next Rank: 500 Posts; Posts: 113; Joined: Sun Nov 24, 2013 9:19 pmFollowed by: 5 members; Thanked: 1 times

by bml1105 » Sun Dec 22, 2013 5:25 pm

Thanks! I see it now.

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