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# Which of the following is the value of sqrt 3 0.000064

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Intern
Joined: 27 Sep 2011
Posts: 13
GMAT Date: 12-15-2011
Which of the following is the value of sqrt 3 0.000064  [#permalink]

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02 Oct 2011, 19:08
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Difficulty:

25% (medium)

Question Stats:

59% (00:26) correct 41% (00:16) wrong based on 253 sessions

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Which of the following is the value of $$\sqrt[3]{0.000064}$$

A) 0.004
B) 0.008
C) 0.02
D) 0.04
E) 0.2

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-is-the-value-of-root-3rd-rt-136562.html
Manager
Joined: 12 May 2011
Posts: 93
Location: United States
Concentration: Finance, Marketing
GMAT 1: 730 Q47 V44

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02 Oct 2011, 20:23
I'm not quite sure what the question is actually asking- to me, it seems as though it's (0.000064) ^ (1 / 3), which should be equal to 0.04 (D).
Current Student
Joined: 08 Jan 2009
Posts: 300
GMAT 1: 770 Q50 V46

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02 Oct 2011, 20:57
1
I think the best way to approach these questions is to employ a systematic approach - it's very easy to misplace a decimal or make a silly mistake.

$$\sqrt[3]{0.000064}$$

$$.000064 = 64 * 10^{-6}$$

$$\sqrt[3]{64 * 10^{-6}} = \sqrt[3]{64} * \sqrt[3]{10^{-6}}$$

$$= 4 *{10^{-2}}$$

$$= .04$$

The Manhattan FDP book covers these types of questions well.
Intern
Joined: 27 Sep 2011
Posts: 13
GMAT Date: 12-15-2011

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03 Oct 2011, 10:54
Thank you all for your answers and information but the question is:
Which of the following is the value of \sqrt{[square_root]3}[/square_root]0.000064?

I'm not able to get the sign right but it has (2) square roots for the number, does that make sense and actually the answer is (E) which is 0.2. I need some help how they got this answer??

Thank you!!
Intern
Joined: 26 May 2011
Posts: 13
Location: United States

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03 Oct 2011, 19:31
1
pike wrote:
I think the best way to approach these questions is to employ a systematic approach - it's very easy to misplace a decimal or make a silly mistake.

$$\sqrt[3]{0.000064}$$

$$.000064 = 64 * 10^{-6}$$

$$\sqrt[3]{64 * 10^{-6}} = \sqrt[3]{64} * \sqrt[3]{10^{-6}}$$

$$= 4 *{10^{-2}}$$

$$= .04$$

The Manhattan FDP book covers these types of questions well.

good explanation.
Manager
Joined: 20 Aug 2011
Posts: 125
Re: Which of the following is the value of 3 root  [#permalink]

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04 Oct 2011, 12:47
1
the question is: [(.000064)^1/3]^1/2

cynthiap wrote:
Thank you all for your answers and information but the question is:
Which of the following is the value of \sqrt{[square_root]3}[/square_root]0.000064?

I'm not able to get the sign right but it has (2) square roots for the number, does that make sense and actually the answer is (E) which is 0.2. I need some help how they got this answer??

Thank you!!

No it doesn't make sense. The outer operation is a square root operation and the inner operator is a cube root.
You really have to learn these basic operations.

They first found the cube root of .000064.
An easy way to write this is 64*10^-6 as most of us are more comfortable with integers than with fractions.
The cube root of (64*10^-6) can be written as (64*10^-6)^1/3 which solves into (64^1/3)*(10^-6)^1/3
or 4*10^-2 (i)

The next step is to take the square root of the (i)
that can be written as (4*10^-2)^1/2
or (4^1/2)*(10^-2)^1/2
or 2^10^-1
or 0.2

Hence E
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Intern
Joined: 27 Sep 2011
Posts: 13
GMAT Date: 12-15-2011
Re: Which of the following is the value of 3 root  [#permalink]

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04 Oct 2011, 15:24
Thank you blink005! I understand it has root square and and cube root. I don't understand how you were able to get 10 after moving the decimal? basically getting 64*10^-6??

Thank you for your patience and assistance!
Manager
Joined: 20 Aug 2011
Posts: 125
Re: Which of the following is the value of 3 root  [#permalink]

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04 Oct 2011, 18:49
cynthiap wrote:
Thank you blink005! I understand it has root square and and cube root. I don't understand how you were able to get 10 after moving the decimal? basically getting 64*10^-6??

Thank you for your patience and assistance!

Simple examples again-

50=5*10
500=5*100 =5*10*10 =5*(10^2)
0.5=5/10 =5*1/10 =5*10^-1
0.05=5/100=5*1/100 =5*10^-2

.000064=64/10^6 =64*1/10^6= 64*10^-6
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Re: Which of the following is the value of 3 root  [#permalink]

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05 Oct 2011, 00:48
cynthiap wrote:
Hi ya'll,

Coming across some road bumps with the arithmetic part of the GMAT, for example Operations on radical expressions. I have this question, which I don't understand how they got that answer.

From the GMAT Review 12th Edition (page 153) Q11

Which of the following is the value of \sqrt{3}0.000064

A) 0.004
B) 0.008
C) 0.02
D) 0.04
E) 0.2

Any help will be much appreciated it, the book only covers the answer but I am not understanding the formula.

For basics of exponents and roots, check out these posts:

http://www.veritasprep.com/blog/2011/07 ... eparation/
http://www.veritasprep.com/blog/2011/07 ... ration-ii/
http://www.veritasprep.com/blog/2011/07 ... s-applied/
http://www.veritasprep.com/blog/2011/08 ... -the-gmat/
http://www.veritasprep.com/blog/2011/08 ... exponents/
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Re: Which of the following is the value of 3 root  [#permalink]

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05 Oct 2011, 03:37
Thanks for the clear up
Math Expert
Joined: 02 Sep 2009
Posts: 55715
Re: Which of the following is the value of sqrt 3 0.000064  [#permalink]

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04 Feb 2014, 10:01
cynthiap wrote:
Which of the following is the value of $$\sqrt[3]{0.000064}$$

A) 0.004
B) 0.008
C) 0.02
D) 0.04
E) 0.2

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-is-the-value-of-root-3rd-rt-136562.html
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Math Expert
Joined: 02 Sep 2009
Posts: 55715
Re: Which of the following is the value of sqrt 3 0.000064  [#permalink]

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04 Feb 2014, 10:02
2
1
Which of the following is the value of $$\sqrt{\sqrt[3]{0.000064}}$$

(A) 0.004
(B) 0.008
(C) 0.02
(D) 0.04
(E) 0.2

There are many ways to solve this problem, for example:

$$\sqrt{\sqrt[3]{0.000064}}=\sqrt[6]{0.000064}=\sqrt[6]{\frac{2^6}{10^6}}=\frac{2}{10}=0.2$$.

For theory on exponents and roots check:
math-number-theory-88376.html

For practice on exponents and roots check:
tough-and-tricky-exponents-and-roots-questions-125967.html (DS problems)
tough-and-tricky-exponents-and-roots-questions-125956.html (PS problems)

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-is-the-value-of-root-3rd-rt-136562.html
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Re: Which of the following is the value of sqrt 3 0.000064  [#permalink]

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19 Sep 2018, 02:00
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Re: Which of the following is the value of sqrt 3 0.000064   [#permalink] 19 Sep 2018, 02:00
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