What is the value of sqrt (x)? EXPERTS PLEASE HELP !!

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apoorva.srivastva: Master | Next Rank: 500 Posts; Posts: 146; Joined: Wed Aug 27, 2008 5:41 am; Thanked: 3 times

by apoorva.srivastva » Mon Jun 22, 2009 10:13 pm

If √x is an integer, what is the value of √x?

1.) 11<x<17
2.) 2<√x<5

Kindly tell me when do we consider only the positive square root of a variable.....

According to me if x>0 and x=16 then √x will be only 4 and not 4 and (-4 ) both....

And if X<0 then we consider both the positive and negative roots...Please correct me if i am wrong!!

please clear this confusion of mine!!!!

Regards,
Apoorva

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Source: Beat The GMAT — Data Sufficiency | Mon Jun 22, 2009 10:13 pm

mikeCoolBoy: Master | Next Rank: 500 Posts; Posts: 119; Joined: Tue Jan 20, 2009 10:16 pm; Thanked: 9 times; GMAT Score:730

by mikeCoolBoy » Mon Jun 22, 2009 10:29 pm

in GMAT land you only consider square root of a positive number so x cannot be negative if you try to calculate sqrt(x).

Answering your question if x = 16 sqrt(x) = 4 or -4

then for the question you posted.
sqrt(x) is integer so x is integer as well.

statement 1 tell us that x is between 11 and 17

so x is in the set {12,13,14,15,16} only x = 16 has square root integer sqrt(x) = 4 or sqrt(x) = -4 insufficient

statement 2 tell us that sqrt(x) is between 2 and 5

so sqrt(x) = 3 or 4 insufficient

both statements make sqrt(x) = 4 so answer should be C

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apoorva.srivastva: Master | Next Rank: 500 Posts; Posts: 146; Joined: Wed Aug 27, 2008 5:41 am; Thanked: 3 times

by apoorva.srivastva » Mon Jun 22, 2009 10:56 pm

[quote="mikeCoolBoy"]in GMAT land you only consider square root of a positive number so x cannot be negative if you try to calculate sqrt(x).

Answering your question if x = 16 sqrt(x) = 4 or -4

then for the question you posted.
sqrt(x) is integer so x is integer as well.

statement 1 tell us that x is between 11 and 17

so x is in the set {12,13,14,15,16} only x = 16 has square root integer sqrt(x) = 4 or sqrt(x) = -4 insufficient

statement 2 tell us that sqrt(x) is between 2 and 5

so sqrt(x) = 3 or 4 insufficient

both statements make sqrt(x) = 4 so answer should be C[/quote]

But here 16 is a positive number so sqrt of 16 shud be 4

I am still not clear!!

in this case since (-4)^2 and 4^2 both give 16 ...the sqrt of 16 will have both roots .....please help me with an example which has only one positive root

please this may sound silly but please clarify :)

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rah_pandey: Master | Next Rank: 500 Posts; Posts: 122; Joined: Fri May 22, 2009 10:38 pm; Thanked: 8 times; GMAT Score:700

by rah_pandey » Tue Jun 23, 2009 12:00 am

in this case since (-4)^2 and 4^2 both give 16 ...the sqrt of 16 will have both roots .....please help me with an example which has only one positive root

First of all there is a difference between

x^2=16

and

x=root(16)

in case I x can have two possible values +4,-4 as we now write x=+/-root(16)

If you are getting confused. factorise and solve
(x-4)*(x+4)=0=> x=4 or -4

please note root(z) does not itself mean the value is -ve also. we need to specify it

where as in case II root(16)=+4 strictly

To simply put if we write 2 than it implies +2
root(x) is also a number and so only positive value dont confuse between the two cases discussed above.

IN A NUTSHELL
ROOT IS SIGN NEUTRAL.BY ITSELF IT DOES NOT MEAN POSITIVE OR NEGATIVE.

Last edited by rah_pandey on Tue Jun 23, 2009 12:13 am, edited 1 time in total.

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joymukhi: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Sat May 02, 2009 3:27 pm

by joymukhi » Tue Jun 23, 2009 12:11 am

Hi rah,
One question then, in the explanation above, square root of x would mean square root of a positive integer 16 which would mean only a single positive value 4? Why do we have to consider two values of +4 and -4 then? Appreciate if someone can clarify.

Thanks,
Jay

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rah_pandey: Master | Next Rank: 500 Posts; Posts: 122; Joined: Fri May 22, 2009 10:38 pm; Thanked: 8 times; GMAT Score:700

by rah_pandey » Tue Jun 23, 2009 12:25 am

Hi rah,
One question then, in the explanation above, square root of x would mean square root of a positive integer 16 which would mean only a single positive value 4? Why do we have to consider two values of +4 and -4 then? Appreciate if someone can clarify.

Thanks,
Jay

First of all sqrt(x)=> x > 0 in real world.(GMAT world) since root of a negative number is non real , a complex quantity which we do not consider in GMAT

also if z^2=x than z can take any of the positive or negative value(but x can be positive only)

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deltaforce: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue May 26, 2009 5:30 am; Thanked: 2 times

hmmm

by deltaforce » Tue Jun 23, 2009 7:54 am

is it just me or sqrt just got complicated in this post....so whats the answer

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rah_pandey: Master | Next Rank: 500 Posts; Posts: 122; Joined: Fri May 22, 2009 10:38 pm; Thanked: 8 times; GMAT Score:700

by rah_pandey » Tue Jun 23, 2009 8:03 am

i think this will clear your doubts since it is from an official source

https://www.manhattangmat.com/forums/ps- ... t6947.html

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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 » Tue Jun 23, 2009 12:02 pm

Here's the simple rule:

By mathematical convention, "√" literally translates as "the positive square root of". Whenever you see the "√" symbol on the GMAT, you are only looking at the positive root.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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apoorva.srivastva: Master | Next Rank: 500 Posts; Posts: 146; Joined: Wed Aug 27, 2008 5:41 am; Thanked: 3 times

by apoorva.srivastva » Tue Jun 23, 2009 12:07 pm

Thanks Stuart for pointing out the rule!!!

But if X^2 =9 ..can we take square root on both the sides and say x = 3!!!

OR

if sqrt (x) = 3

then can we say squaring both the sides we get x = 9

Please clarify on this

Thanks and Regards,
Apoorva

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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 » Tue Jun 23, 2009 1:20 pm

apoorva.srivastva wrote:Thanks Stuart for pointing out the rule!!!

But if X^2 =9 ..can we take square root on both the sides and say x = 3!!!

OR

if sqrt (x) = 3

then can we say squaring both the sides we get x = 9

Please clarify on this

Thanks and Regards,
Apoorva

You ask a great question, because it's essential to understand the difference, especially in data sufficiency.

Let's make up a DS question to illustrate the difference:

Q: What's the value of x?

(1) x = √9

(2) x^2 = 9

Step 1 of the Kaplan Method for DS: focus on the question stem.

We're asked for the value of x; not much to think about here. We need 1 and only 1 value for a statement to be sufficient and, as of right now, we have no restrictions on x at all.

Step 2 of the Kaplan Method for DS: consider each statement by itself, in conjunction with the stem.

(1) we know that the "√" sign means "postive root of". 9 only has one positive root: 3. Therefore, x must be 3... sufficient.

(2) we know that if x^2 = 9, x could be +/- 3... 2 possible values, therefore insufficient.

As an algebraic aside, here's the "official" way to solve this equation:

x^2 = 9
x^2 - 9 = 0
(x + 3)(x - 3) = 0
x = -3 or +3

(1) is sufficient and (2) is insufficient: no need to combine, select (A).

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apoorva.srivastva: Master | Next Rank: 500 Posts; Posts: 146; Joined: Wed Aug 27, 2008 5:41 am; Thanked: 3 times

by apoorva.srivastva » Tue Jun 23, 2009 1:31 pm

Thanks Stuart for you effort to clear my doubt!!!

Just one more clarification before i shut up!!! ;)

If the question asks us to find the value of x, where x is an integer and we are given that .......Sqrt ( x) = 3

then x = 3^2 = 9

Is my reasoning correct!!!

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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 » Tue Jun 23, 2009 5:19 pm

apoorva.srivastva wrote:Thanks Stuart for you effort to clear my doubt!!!

Just one more clarification before i shut up!!!

If the question asks us to find the value of x, where x is an integer and we are given that .......Sqrt ( x) = 3

then x = 3^2 = 9

Is my reasoning correct!!!

Correct!

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Domnu: Master | Next Rank: 500 Posts; Posts: 385; Joined: Sun May 24, 2009 3:55 pm; Thanked: 11 times; GMAT Score:740

by Domnu » Thu Jun 25, 2009 1:47 pm

Btw, I don't think the answer is C... the answer should be A.

If sqrt(x) is an integer, then x has to be an integer. So, x = 12, 13, 14, 15, 16 only. But 16 is the only perfect square, and sqrt(16) = 4 (not -4). So, the answer is A.

If you know what imaginary numbers are, this is where they come in. But if you're not sure what this is, then never mind.

Have you wondered how you could have found such a treasure? -T

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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Sun Jun 28, 2009 10:24 am

A for me too..

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