0.0001^(1/2)

Question

\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}

Abhishek009 · Accepted Answer

\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

Resad95 · Answer

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

lalania1 · Answer

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.

BrentGMATPrepNow · Answer

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

So, √0.00001 = √(1/100,000)
= (√1)/(√100,000)    
= 1/( √100,000 )

Let's take a closer look at  √100,000  
 √100,000  =  √(10,000 x 10) 
=  (√10,000)(√10)     
=  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

Princ · Answer

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}

chetan2u · Answer

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

C

EgmatQuantExpert · Answer

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

T1101 · Answer

\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

Kimberly77 · Answer

Hi  BrentGMATPrepNow , √ 1 * 10^-4 = 10^-2 = 1/100. What have I missed here? Thanks Brent.

BrentGMATPrepNow · Answer

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)}

Kimberly77 · Answer

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)

BrentGMATPrepNow · Answer

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)

Kimberly77 · Answer

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.

KarishmaB · Answer

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:

https://www.youtube.com/watch?v=ibDqnatAMG8

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0.0001^(1/2)

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0.0001^(1/2)

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards