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0.0001^(1/2)

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lalania1
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0.0001^(1/2) [#permalink] New post  24 Nov 2016, 07:31
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55% (hard)

Question Stats:

61% (01:21) correct 39% (01:19) wrong based on 391 sessions

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\(\sqrt{0.00001}\) ?


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

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

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

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

E) \(\frac{\sqrt{10}}{10000}\)
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Abhishek009
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Re: 0.0001^(1/2) [#permalink] New post  24 Nov 2016, 07:51
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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
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Re: 0.0001^(1/2) [#permalink] New post  24 Nov 2016, 08:00
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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
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Re: 0.0001^(1/2) [#permalink] New post  24 Nov 2016, 08:37
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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.
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Capture.PNG [ 593.3 KiB | Viewed 8812 times ]

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BrentGMATPrepNow
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0.0001^(1/2) [#permalink] New post  Updated on: 28 Oct 2022, 05:50
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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
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Originally posted by BrentGMATPrepNow on 24 Nov 2016, 10:41.
Last edited by BrentGMATPrepNow on 28 Oct 2022, 05:50, edited 1 time in total.
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Re: 0.00001^(1/2) = [#permalink] New post  18 Jul 2018, 00:02
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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 \(\sqrt{10}\)
\(\frac{{1}}{{100\sqrt{10}}}\)\(*\)\(\frac{{\sqrt[]{10}}}{{\sqrt[]{10}}}\) \(=\frac{{\sqrt[]{10}}}{1000}\)
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chetan2u
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Re: 0.00001^(1/2) = [#permalink] New post  18 Jul 2018, 00:12
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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
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0.00001^(1/2) = [#permalink] New post  18 Jul 2018, 03:59
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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
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Re: 0.0001^(1/2) [#permalink] New post  10 Sep 2018, 02:00
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\(\sqrt{0.00001}\)

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

=\(\sqrt{10^{-6}*10}\) --> 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
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Re: 0.0001^(1/2) [#permalink] New post  28 Oct 2022, 05:28
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


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Hi BrentGMATPrepNow, √ 1 * 10^-4 = 10^-2 = 1/100. What have I missed here? Thanks Brent.
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Re: 0.0001^(1/2) [#permalink] New post  28 Oct 2022, 05:57
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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, \(\sqrt{10} * 10^{-4} = 10^{1/2} * 10^{-4} = 10^{(1/2)+(-4)}\)
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I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
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Re: 0.0001^(1/2) [#permalink] New post  28 Oct 2022, 06:38
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)
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BrentGMATPrepNow
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Re: 0.0001^(1/2) [#permalink] New post  28 Oct 2022, 06:55
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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)
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Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
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Kimberly77
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Re: 0.0001^(1/2) [#permalink] New post  28 Oct 2022, 07:03
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.
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Re: 0.0001^(1/2) [#permalink]
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