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0.0001^(1/2)

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0.0001^(1/2)  [#permalink]

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New post 24 Nov 2016, 07:31
10
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (00:56) correct 41% (00:49) wrong based on 303 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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Re: 0.0001^(1/2)  [#permalink]

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New post 24 Nov 2016, 07:51
1
4
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]

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New post 24 Nov 2016, 08:00
1
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


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Re: 0.0001^(1/2)  [#permalink]

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New post 24 Nov 2016, 08:37
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

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Capture.PNG [ 593.3 KiB | Viewed 2742 times ]

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Re: 0.0001^(1/2)  [#permalink]

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New post 24 Nov 2016, 10:41
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:

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Re: 0.00001^(1/2) =  [#permalink]

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New post 18 Jul 2018, 00:02
1
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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Re: 0.00001^(1/2) =  [#permalink]

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New post 18 Jul 2018, 00:12
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]

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New post 18 Jul 2018, 03:59
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]

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New post 10 Sep 2018, 02:00
\(\sqrt{0.00001}\)

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

=\(\sqrt{10^{-6}*10}\) --> 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) &nbs [#permalink] 10 Sep 2018, 02:00
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