NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 06:54 It is currently 25 Apr 2024, 06:54
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

0.0001^(1/2)

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
lalania1
Manager
Manager
Joined: 17 Nov 2013
Posts: 65
Own Kudos [?]: 241 [26]
Given Kudos: 19
Send PM
GMAT ToolKit User
0.0001^(1/2) [#permalink] New post   24 Nov 2016, 08:31
1
Kudos
25
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

62% (01:21) correct 38% (01:20) wrong based on 504 sessions
Hide Show timer Statistics
\(\sqrt{0.00001}\) ?


A) \(\frac{\sqrt{10}}{100}\)

B) \(\frac{1}{100}\)

C) \(\frac{\sqrt{10}}{1000}\)

D) \(\frac{1}{1000}\)

E) \(\frac{\sqrt{10}}{10000}\)
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6072
Own Kudos [?]: 4689 [8]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: 0.0001^(1/2) [#permalink] New post   24 Nov 2016, 08:51
3
Kudos
5
Bookmarks
lalania1 wrote:
\(\sqrt{0.00001}\) ?

A) \(\sqrt{10}\)/100

B) 1/100

C) \(\sqrt{10}\)/1000

D) 1/1000

E) \(\sqrt{10}\)/10000


\(\sqrt{0.00001}\)

= \(\sqrt{\frac{1}{100000}}\)

= \(\sqrt{\frac{10}{1000000}}\)

= \(\sqrt{\frac{10}{10^6}}\)

= \(\frac{√10}{10^3}\)

Hence, answer will be (C) \(\sqrt{10}\)/1000
General Discussion
User avatar
B
Resad95
Intern
Intern
Joined: 11 Sep 2016
Posts: 39
Own Kudos [?]: 41 [3]
Given Kudos: 126
Location: Ukraine
Concentration: Finance, General Management
GMAT 1: 570 Q44 V27
GPA: 3.11
WE:Accounting (Accounting)
Send PM
GMAT ToolKit User
Re: 0.0001^(1/2) [#permalink] New post   24 Nov 2016, 09:00
2
Kudos
1
Bookmarks
lalania1 wrote:
\(\sqrt{0.00001}\) ?

A) \(\sqrt{10}\)/100

B) 1/100

C) \(\sqrt{10}\)/1000

D) 1/1000

E) \(\sqrt{10}\)/10000


Rewrite equation as \(\sqrt{1*10^{-5}}\), where 1 will come out as 1 and \(10^{-5}\) is \(10^{-4}*10^{-1}\) when divided by 2 ( square root) will be \(10^{-2}*10^{-1/2}\)

\(1/{100*\sqrt{10}}\)

to get rid of square root in denominator we multiply both sides with \(\sqrt{10}\) and get \(\sqrt{10}/{100*10}\).
Answer C


+1 If you liked it :P
User avatar
G
T1101
Manager
Manager
Joined: 07 Aug 2018
Posts: 88
Own Kudos [?]: 251 [2]
Given Kudos: 247
Location: United States (MA)
GMAT 1: 560 Q39 V28
GMAT 2: 670 Q48 V34
Send PM
Re: 0.0001^(1/2) [#permalink] New post   10 Sep 2018, 03:00
2
Bookmarks
\(\sqrt{0.00001}\)

=\(\sqrt{10^{-5}*1}\)

=\(\sqrt{10^{-6}*10}\) --> Easier to get \(10^{-6}\) out of the square root

=\(10^{-3}\)*\(\sqrt{10}\)

=\(\frac{1}{10^3}\)*\(\sqrt{10}\)

=\(\frac{1}{1000}\)*\(\sqrt{10}\)

=\(\sqrt{10}\)/1000
avatar
lalania1
Manager
Manager
Joined: 17 Nov 2013
Posts: 65
Own Kudos [?]: 241 [1]
Given Kudos: 19
Send PM
GMAT ToolKit User
Re: 0.0001^(1/2) [#permalink] New post   24 Nov 2016, 09:37
1
Bookmarks
the answer is attached. this question was tricky because the exponents and roots component. thanks for your responses, you helped me to better understand this problem.
Attachments

Capture.PNG
Capture.PNG [ 593.3 KiB | Viewed 11524 times ]

User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29925 [1]
Given Kudos: 799
Location: Canada
Send PM
0.0001^(1/2) [#permalink] New post   Updated on: 28 Oct 2022, 06:50
1
Kudos
Expert Reply
Top Contributor
lalania1 wrote:
\(\sqrt{0.00001}\) ?

A) \(\sqrt{10}\)/100

B) 1/100

C) \(\sqrt{10}\)/1000

D) 1/1000

E) \(\sqrt{10}\)/10000


Rule #1: √(a/b) = (√a)/(√b)
Rule #2: √(ab) = (√a)(√b)

So, √0.00001 = √(1/100,000)
= (√1)/(√100,000) [applied rule #1]
= 1/(√100,000)

Let's take a closer look at √100,000
√100,000 = √(10,000 x 10)
= (√10,000)(√10) [applied rule #2]
= 100(√10)

So, 1/(√100,000) = 1/100√10
Check the answer choices...not there.
Looks like we need to "fix" (rationalize) the denominator (for more on this, check the video below)
Multiply top and bottom by √10 to get: (√10)(1)/(√10)(100√10)
Simplify: (√10)/1000

Answer: C

Originally posted by BrentGMATPrepNow on 24 Nov 2016, 11:41.
Last edited by BrentGMATPrepNow on 28 Oct 2022, 06:50, edited 1 time in total.
User avatar
D
Princ
Senior Manager
Senior Manager
Joined: 22 Feb 2018
Posts: 355
Own Kudos [?]: 799 [1]
Given Kudos: 34
Send PM
Re: 0.00001^(1/2) = [#permalink] New post   18 Jul 2018, 01:02
1
Kudos
Bunuel wrote:
\(\sqrt{0.00001}\) =


A) \(\frac{\sqrt{10}}{100}\)

B) \(\frac{1}{100}\)

C) \(\frac{\sqrt{10}}{1000}\)

D) \(\frac{1}{1000}\)

E) \(\frac{\sqrt{10}}{10000}\)


OA: C
\(\sqrt{0.00001}\) = \(\sqrt{10^{-5}}=10^{-2}*10^{-\frac{{1}}{{2}}}= \frac{1}{{100\sqrt{10}}}\)
Multiplying numerator and denominator by \(\sqrt{10}\)
\(\frac{{1}}{{100\sqrt{10}}}\)\(*\)\(\frac{{\sqrt[]{10}}}{{\sqrt[]{10}}}\) \(=\frac{{\sqrt[]{10}}}{1000}\)
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16833 [1]
Given Kudos: 165
Send PM
0.00001^(1/2) = [#permalink] New post   18 Jul 2018, 04:59
1
Bookmarks
Expert Reply
Approach and Working:

\(\sqrt{(0.00001)}= \sqrt{(1/10^5)}= \sqrt{(10/10^6)}= \frac{\sqrt{10}}{ 10^3}= \frac{\sqrt{10}}{ 1000}\)

Hence, the correct answer is option C.

Answer: C
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14822
Own Kudos [?]: 64911 [1]
Given Kudos: 426
Location: Pune, India
Send PM
0.0001^(1/2) [#permalink] New post   05 Dec 2023, 02:08
1
Bookmarks
Expert Reply
lalania1 wrote:
\(\sqrt{0.00001}\) ?


A) \(\frac{\sqrt{10}}{100}\)

B) \(\frac{1}{100}\)

C) \(\frac{\sqrt{10}}{1000}\)

D) \(\frac{1}{1000}\)

E) \(\frac{\sqrt{10}}{10000}\)


Here is how one can approach it: We see that the options do not have any decimals. So let's get rid of the decimal.

\(\sqrt{0.00001} = \sqrt{\frac{1}{100000}} = \frac{1}{100\sqrt(10)} \)

Now note that it doesn't match any option but some options have root 10 in the numerator. So multiply and divide by sqrt(10) to get

\(\frac{1*\sqrt(10)}{100\sqrt(10) * \sqrt(10)} = \frac{\sqrt(10)}{1000}\)

Answer (C)

Check out this video on exponents:

User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31918 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: 0.00001^(1/2) = [#permalink] New post   18 Jul 2018, 01:12
Expert Reply
Bunuel wrote:
\(\sqrt{0.00001}\) =


A) \(\frac{\sqrt{10}}{100}\)

B) \(\frac{1}{100}\)

C) \(\frac{\sqrt{10}}{1000}\)

D) \(\frac{1}{1000}\)

E) \(\frac{\sqrt{10}}{10000}\)


\(\sqrt{0.00001}........................\sqrt{\frac{1}{100000}}=\frac{1}{100}*\sqrt{\frac{1}{10}}.........................\frac{\sqrt{10}}{1000}\)

C
User avatar
S
Kimberly77
Senior Manager
Senior Manager
Joined: 16 Nov 2021
Posts: 476
Own Kudos [?]: 27 [0]
Given Kudos: 5900
Location: United Kingdom
Send PM
Re: 0.0001^(1/2) [#permalink] New post   28 Oct 2022, 06:28
BrentGMATPrepNow wrote:
lalania1 wrote:
\(\sqrt{0.00001}\) ?

A) \(\sqrt{10}\)/100

B) 1/100

C) \(\sqrt{10}\)/1000

D) 1/1000

E) \(\sqrt{10}\)/10000


Rule #1: √(a/b) = (√a)/(√b)
Rule #2: √(ab) = (√a)(√b)

So, √0.00001 = √(1/100,000)
= (√1)/(√100,000) [applied rule #1]
= 1/(√100,000)

Let's take a closer look at √100,000
√100,000 = √(10,000 x 10)
= (√10,000)(√10) [applied rule #2]
= 100(√10)

So, 1/(√100,000) = 1/100√10
Check the answer choices...not there.
Looks like we need to "fix" (rationalize) the denominator (for more on this, check the video below)
Multiply top and bottom by √10 to get: (√10)(1)/(√10)(100√10)
Simplify: (√10)/1000
Answer:
Show Spoiler
C


RELATED VIDEOS





Hi BrentGMATPrepNow, √ 1 * 10^-4 = 10^-2 = 1/100. What have I missed here? Thanks Brent.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29925 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: 0.0001^(1/2) [#permalink] New post   28 Oct 2022, 06:57
Expert Reply
Top Contributor
Kimberly77 wrote:
Hi BrentGMATPrepNow, √ 1 * 10^-4 = 10^-2 = 1/100. What have I missed here? Thanks Brent.


What exponent rule are you applying here?

First, √1 = 1, which means you are saying √1 * 10^-4 = 1 * 10^-4 = 10^-2, which isn't true.

Did you mean to write √10 and not √1?
Even if that's the case, the exponent property you'd need to use is: \(x^a * x^b = x^{a+b}\)

So, \(\sqrt{10} * 10^{-4} = 10^{1/2} * 10^{-4} = 10^{(1/2)+(-4)}\)
User avatar
S
Kimberly77
Senior Manager
Senior Manager
Joined: 16 Nov 2021
Posts: 476
Own Kudos [?]: 27 [0]
Given Kudos: 5900
Location: United Kingdom
Send PM
Re: 0.0001^(1/2) [#permalink] New post   28 Oct 2022, 07:38
BrentGMATPrepNow wrote:
Kimberly77 wrote:
Hi BrentGMATPrepNow, √ 1 * 10^-4 = 10^-2 = 1/100. What have I missed here? Thanks Brent.


What exponent rule are you applying here?

First, √1 = 1, which means you are saying √1 * 10^-4 = 1 * 10^-4 = 10^-2, which isn't true.

Did you mean to write √10 and not √1?
Even if that's the case, the exponent property you'd need to use is: \(x^a * x^b = x^{a+b}\)

So, \(\sqrt{10} * 10^{-4} = 10^{1/2} * 10^{-4} = 10^{(1/2)+(-4)}\)


Thanks Brent BrentGMATPrepNow for your quick reply.
Since question given is √0.00001. Therefore I'm trying to calculate it with 1 instead of 10? Is that possible?
√1 * 10^-4 = 10^-2 ( 10^-4 is under the same square root as 1 here)
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29925 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: 0.0001^(1/2) [#permalink] New post   28 Oct 2022, 07:55
Expert Reply
Top Contributor
Kimberly77 wrote:
BrentGMATPrepNow wrote:
Kimberly77 wrote:
Hi BrentGMATPrepNow, √ 1 * 10^-4 = 10^-2 = 1/100. What have I missed here? Thanks Brent.


What exponent rule are you applying here?

First, √1 = 1, which means you are saying √1 * 10^-4 = 1 * 10^-4 = 10^-2, which isn't true.

Did you mean to write √10 and not √1?
Even if that's the case, the exponent property you'd need to use is: \(x^a * x^b = x^{a+b}\)

So, \(\sqrt{10} * 10^{-4} = 10^{1/2} * 10^{-4} = 10^{(1/2)+(-4)}\)


Thanks Brent BrentGMATPrepNow for your quick reply.
Since question given is √0.00001. Therefore I'm trying to calculate it with 1 instead of 10? Is that possible?
√1 * 10^-4 = 10^-2 ( 10^-4 is under the same square root as 1 here)


Using brackets will help avoid any ambiguity in the future.
One problem with your solution is that 0.00001 = 1 x 10^(-5), and not 1 x 10^(-4)

See how your calculations go with 1 x 10^(-5)
User avatar
S
Kimberly77
Senior Manager
Senior Manager
Joined: 16 Nov 2021
Posts: 476
Own Kudos [?]: 27 [0]
Given Kudos: 5900
Location: United Kingdom
Send PM
Re: 0.0001^(1/2) [#permalink] New post   28 Oct 2022, 08:03
Thanks BrentGMATPrepNow, so error here is I'v got 1 zero less in calculation and yes it works now. You're a STAR and thanks Brent.
GMAT Club Bot
gmatclubot
Re: 0.0001^(1/2) [#permalink]
28 Oct 2022, 08:03
Moderators:
Bunuel
Math Expert
92912 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions