GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 14 Oct 2019, 11:39

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Why cant the square root of 4 be -2?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
S
Joined: 10 Dec 2011
Posts: 81
Location: India
Concentration: Finance, Economics
GMAT Date: 09-28-2012
WE: Accounting (Manufacturing)
Why cant the square root of 4 be -2?  [#permalink]

Show Tags

New post 08 Jan 2018, 22:10
Why cannot the square root of 4 be -2?

When x^2 = 4, then x can be + or -2. But when x = (4)^1/2, then x = 2 only... Why?
-2 * -2 = 4.
Attachments

x=root4.PNG
x=root4.PNG [ 4.27 KiB | Viewed 728 times ]

x=root4.PNG
x=root4.PNG [ 2.48 KiB | Viewed 731 times ]

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58320
Re: Why cant the square root of 4 be -2?  [#permalink]

Show Tags

New post 08 Jan 2018, 23:10
talismaaniac wrote:
Why cannot the square root of 4 be -2?

When x^2 = 4, then x can be + or -2. But when x = (4)^1/2, then x = 2 only... Why?
-2 * -2 = 4.


\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.

Image
The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).

Attachment:
600px-Square_root_0_25.svg.png
600px-Square_root_0_25.svg.png [ 11.45 KiB | Viewed 11011 times ]

_________________
Manager
Manager
avatar
S
Joined: 10 Dec 2011
Posts: 81
Location: India
Concentration: Finance, Economics
GMAT Date: 09-28-2012
WE: Accounting (Manufacturing)
Re: Why cant the square root of 4 be -2?  [#permalink]

Show Tags

New post 08 Jan 2018, 23:34
Bunuel wrote:

TO SUMMARIZE:
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).



I think I do understand some of this. Much Thanks!! :-)
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 833
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Why cant the square root of 4 be -2?  [#permalink]

Show Tags

New post 14 Jan 2018, 14:25
Bunuel wrote:
talismaaniac wrote:
Why cannot the square root of 4 be -2?

When x^2 = 4, then x can be + or -2. But when x = (4)^1/2, then x = 2 only... Why?
-2 * -2 = 4.


Check this out: https://www.manhattanprep.com/gmat/blog ... -the-gmat/

The short explanation is that it's somewhat arbitrary - there are mathematical reasons for thinking about it that way that aren't really important on the GMAT. It's one of those things that you can (and should) just memorize, since the GMAT will be very predictable. But the article also explains it a bit. :)
_________________
Image

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!
GMAT Club Bot
Re: Why cant the square root of 4 be -2?   [#permalink] 14 Jan 2018, 14:25
Display posts from previous: Sort by

Why cant the square root of 4 be -2?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne