5- root of y to the power of 2

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vidhya16: Master | Next Rank: 500 Posts; Posts: 115; Joined: Thu Mar 24, 2011 3:49 am; Thanked: 1 times

by vidhya16 » Tue Jun 28, 2011 12:58 pm

5 -âˆšyÂ² = -3 .Whats the value of y?

Ta

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Source: Beat The GMAT — Problem Solving | Tue Jun 28, 2011 12:58 pm

Ashley@VeritasPrep: GMAT Instructor; Posts: 199; Joined: Tue May 17, 2011 6:06 amFollowed by: 121 members; Location: Cambridge, MA; Thanked: 192 times; GMAT Score:780

by Ashley@VeritasPrep » Tue Jun 28, 2011 1:02 pm

5 - root(y^2) = -3
5+3 = root(y^2)
8 = root(y^2)
64 = y^2
y = +8 or -8

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Veritas Prep

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vidhya16: Master | Next Rank: 500 Posts; Posts: 115; Joined: Thu Mar 24, 2011 3:49 am; Thanked: 1 times

by vidhya16 » Wed Jun 29, 2011 3:18 am

Thanks Ashley. One quick question. Can we write the equation like

5-y = -3 by canceling square root with square?

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 29, 2011 4:29 am

vidhya16 wrote: One quick question. Can we write the equation like

5-y = -3 by canceling square root with square?

Hi,
Square root of a number is always the positive root.
So, sqrt(y^2) = |y|
Example: sqrt((-3)^2) = |-3| = 3
sqrt(3^2) = |3| = 3
So you can write 5-sqrt(y^2) as 5 - |y|
Now solve, 5 - |y| = -3 =>|y| = 8. So, y = 8 or -8.

Cheers!

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Jun 29, 2011 4:44 am

vidhya16 wrote:5 -âˆšyÂ² = -3 .Whats the value of y?

Ta

âˆšyÂ² = |y|
so 5 -âˆšyÂ² = -3 -> 5 -|y| = -3
case 1: if y>0, 5-y = -3 -> y= 8
case 2: if y<0, 5-(-y) = -3 -> y=-8

so y = 8 or -8.

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Jun 29, 2011 4:47 am

vidhya16 wrote:Thanks Ashley. One quick question. Can we write the equation like

5-y = -3 by canceling square root with square?

since âˆšyÂ² is positive so you can't write âˆšyÂ² = y as we don't know whether y is positive or not but we certainly know that âˆšyÂ² is positive.

so we can write âˆšyÂ² = |y|
hence âˆšyÂ² = y if y>0.
and âˆšyÂ² = -y if y<0.

I hope it is clear ..if not try some numerical values ..

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Ashley@VeritasPrep: GMAT Instructor; Posts: 199; Joined: Tue May 17, 2011 6:06 amFollowed by: 121 members; Location: Cambridge, MA; Thanked: 192 times; GMAT Score:780

by Ashley@VeritasPrep » Wed Jun 29, 2011 8:36 am

Just want to confirm the replies given above -- it's exactly right that you CAN'T simplify root(y^2) to y safely, for precisely the reason explained: if y is negative, root(y^2) will NOT equal y but rather the opposite of y.

I think this problem is a nice illustrator of a good GMAT lesson: if it looks weird, there's probably a reason it needs to. If I came to this problem on the test, I might be inclined to react initially with a sentiment along the lines of "That's silly... why would they write root(y^2) rather than just simply y? That seems indirect, like saying 'I'm not not a girl.'" But then hopefully I'd ponder that some more... like really, why WOULD they write it like that? I'd try to think of a reason. And then I'd realize that it's because "root(y^2)" actually has a different meaning from "y"... and that whether or not you realize that is really the primary thing the problem is testing.

Ashley Newman-Owens
GMAT Instructor
Veritas Prep

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Jun 29, 2011 12:54 pm

Ashley@VeritasPrep wrote:Just want to confirm the replies given above -- it's exactly right that you CAN'T simplify root(y^2) to y safely, for precisely the reason explained: if y is negative, root(y^2) will NOT equal y but rather the opposite of y.

Thanks Ashley for confirming my post...
'I'm not not a girl... hehhehehhe what an example, but what does that exactly mean...

@Frankenstein .. For more simplification I discussed it in my latest post "Is âˆšxÂ² = x or -x or none" on my blog https://mba.webmaggu.com/is-%E2%88%9Ax%C ... x-or-none/ . so check it out.. Hope it would help you a lot, as this is a common confusion among a lots of students...

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Wed Jun 29, 2011 2:19 pm

I also had the same doubt with a similar problem. âˆš (-3)^2 < 0, true or false?

âˆš9 = +3 or -3 so..?

The OA is false as âˆš9 = 3 according to them. I also saw before that when it's âˆšx then it's +x that's wanted. When it's x^2 and you're square rooting then it could be + or - x

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Ashley@VeritasPrep: GMAT Instructor; Posts: 199; Joined: Tue May 17, 2011 6:06 amFollowed by: 121 members; Location: Cambridge, MA; Thanked: 192 times; GMAT Score:780

by Ashley@VeritasPrep » Wed Jun 29, 2011 8:48 pm

MBA.Aspirant wrote:I also had the same doubt with a similar problem. âˆš (-3)^2 < 0, true or false?

âˆš9 = +3 or -3 so..?

The OA is false as âˆš9 = 3 according to them. I also saw before that when it's âˆšx then it's +x that's wanted. When it's x^2 and you're square rooting then it could be + or - x

Yes, so technical the âˆšx means "the principal square root of x," where the word principal means "nonnegative." So the function y = âˆšx is actually only defined over the nonnegative real numbers (that is, both in terms of its domain and in terms of its range). It looks like this -- the graph does not exist in any other quadrants:

In contrast, when you just have y = x^2, or x^2 = 16, or whatever, we don't have that âˆš symbol popping up and meaning "the principal square root." So x can take on any value that will satisfy the equation, and since squaring any negative number always yields the same thing as does squaring its positive counterpart, all equations of this form will have two possible solutions. (That's why we wind up with a parabola in two quadrants instead of just one when we graph y = x^2.)

Ashley Newman-Owens
GMAT Instructor
Veritas Prep

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