February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST We don’t care what your relationship status this year  we love you just the way you are. AND we want you to crush the GMAT! February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST Buy "AllInOne Standard ($149)", get free Daily quiz (2 mon). Coupon code : SPECIAL
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52938

Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
30 Jul 2012, 01:02
Question Stats:
78% (01:05) correct 22% (01:17) wrong based on 2171 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 52938

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
30 Jul 2012, 01:02




Intern
Joined: 27 Jul 2012
Posts: 25

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
30 Jul 2012, 01:39
(E) .02
For simplicity 0.000064 can be \(\frac{64}{1000000}\)
Its cube root would be \(\frac{\sqrt[3]{64}}{\sqrt[3]{1000,000}}\) i.e. \(\frac{4}{100}\)
its square root would be \(\frac{\sqrt[2]{4}}{\sqrt[2]{100}}\) i.e. \(\frac{2}{10}\)
i.e. 0.2




Manager
Joined: 25 Jun 2012
Posts: 62
Location: India
WE: General Management (Energy and Utilities)

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
30 Jul 2012, 02:04
E it is...
= [(64/1000000)^1/3]^1/2 = [(4^3/10^6)^1/3]^1/2 = [ 4/10^2]^1/2 = 2/10 =0.2



Math Expert
Joined: 02 Sep 2009
Posts: 52938

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
03 Aug 2012, 03:59



Math Expert
Joined: 02 Sep 2009
Posts: 52938

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
05 Jun 2013, 03:28



Current Student
Joined: 09 Apr 2013
Posts: 41
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
GPA: 3.55
WE: General Management (NonProfit and Government)

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
05 Jun 2013, 08:06
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
If you know how to do calculations as is, then it is: \(\sqrt{\sqrt[3]{0.000064}} = \sqrt{0.04} = 0.2\)
or
If you know that \(\sqrt{\sqrt[3]{0.000064}} = \sqrt[6]{0.000064}\) and \(2^6 = 64\) Then you can eliminate A, B, and D. Then just move decimals from C and E. C would be 12 decimal places which is WAY too much. 0.2 is 6 which is exactly what you want
Answer is E



Manager
Joined: 27 Apr 2012
Posts: 57
Location: United States
GMAT Date: 06112013
GPA: 3.5
WE: Marketing (Consumer Products)

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
05 Jun 2013, 17:09
The above question can be re written as ((10^6)^1/3)^1/2 * ((64^1/3)^1/2)
= (10^6)^1/6 * (2^6)^1/6
= 10^1 * 2^1 = 0.2



Intern
Joined: 22 Jul 2013
Posts: 16
Concentration: International Business, Marketing
GPA: 3.89

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
02 Feb 2014, 22:19
Could I just clarify something with a solution to this problem? The explanation in the book was given as: 64 * 10^6 under the square root and cubed signs (I can't figure out how to write them in). Then from there it goes down to square root of 4 * 10^2 then 2 * 10^1 which then equals to .2 which is the answer. I think I've figured out how they got from beginning to end by reading the Number Theory post mentioned at the top, but just need clarification. When you have a base to a fraction power like a^n/m that turns to into n root sign a^m correct? So in this case where you have cubed 10^6 it would reverse to 10^6/3 which can be reduced to 10^2 right? I think that's how the book answer went about getting to .2 but would just like clarification. Also this strategy can be used with any large decimaled number that is under a root or cube sign right?
Thanks for your help!



Math Expert
Joined: 02 Sep 2009
Posts: 52938

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
04 Feb 2014, 01:43
amjet12 wrote: Could I just clarify something with a solution to this problem? The explanation in the book was given as: 64 * 10^6 under the square root and cubed signs (I can't figure out how to write them in). Then from there it goes down to square root of 4 * 10^2 then 2 * 10^1 which then equals to .2 which is the answer. I think I've figured out how they got from beginning to end by reading the Number Theory post mentioned at the top, but just need clarification. When you have a base to a fraction power like a^n/m that turns to into n root sign a^m correct? So in this case where you have cubed 10^6 it would reverse to 10^6/3 which can be reduced to 10^2 right? I think that's how the book answer went about getting to .2 but would just like clarification. Also this strategy can be used with any large decimaled number that is under a root or cube sign right?
Thanks for your help! Yes, your reasoning is correct.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Retired Moderator
Joined: 29 Oct 2013
Posts: 257
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
22 May 2014, 11:20
(64/1000000)^1/6={2^(6)/10^(6)}^1/6 = {2^(6*1/6)/10^(6*1/6)}= 2/10= .2
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



Manager
Joined: 12 Feb 2011
Posts: 83

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
19 Aug 2014, 16:16
This is how I tried it the second time  As long as one is able to find the final exponent on the 10 part of the value, one can simply pick the choice that matches that exponent value. In this case 10^(6)*(1/6) = 1/10 = 0.1 and the only choice that has one decimal place is E.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1821
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
19 Aug 2014, 21:04
Bunuel wrote: 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 Practice Questions Question: 9 Page: 153 Difficulty: 650 \(\sqrt{\sqrt[3]{0.000064}} = \sqrt[(2*3)]{\frac{64}{10^6}} = (\frac{2^6}{10^6})^{\frac{1}{6}} = \frac{2}{10} = 0.2\) Answer = E
_________________
Kindly press "+1 Kudos" to appreciate



Manager
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
WE: Analyst (Commercial Banking)

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
09 Dec 2014, 19:26
cube root of 64 is 4. because we need the cube root of 0.000064, 4 needs to have (1/3) as many digits to the right of the decimal as 64, so 0.04.
Similarly, we need the square root of 0.04, so the square root of 4 is 2, but we need half the digits to the right of the decimal, so 0.2



Senior Manager
Joined: 10 Mar 2013
Posts: 498
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
27 Apr 2015, 11:39
> (0,2^6)^1/6 = 0,2
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 674
Location: United States (CA)
Age: 39
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
11 Apr 2016, 15:30
Attached is a visual that should help.
Attachments
Screen Shot 20160411 at 4.29.25 PM.png [ 148.45 KiB  Viewed 14160 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring
Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.)
...or find me on Reddit: http://www.reddit.com/r/GMATpreparation



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
03 May 2016, 07:55
Bunuel wrote: 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
Solution: Let's review the notation first. When an exponent is a fraction, that exponent indicates taking a root. So if we have, for example, 27^1/3, the 1/3 instructs us to take the cube root of 27, which is 3. Similarly, if the exponent were 1/2, such as in 25^1/2, the 1/2 instructs us to take the square root of 25, which is 5. To solve this question, we can refer to two rules: 1) If a decimal with a finite number of decimal places is a perfect cube, its cube root will have exactly onethird of the number of decimal places. Thus, a perfect cube decimal must have a number of decimal places that is a multiple of 3. 2) If a decimal with a finite number of decimal places is a perfect square, its square root will have exactly half of the number of decimal places. Thus, a perfect square decimal must have an even number of decimal places. Let's look first at (0.000064)^1/3. The 1/3 instructs us to take the cube root of 0.000064. By rule number 1, the cube root of 0.000064 = 0.04. We were able obtain this value because 0.000064 has 6 DECIMAL PLACES and because the cube root of 64 is 4. The problem now looks like this: (0.04)^1/2. The ½ instructs us to find the square root of 0.04. By rule number 2, the square root of 0.04 = 0.2. We were able to obtain this value because 0.04 has 2 DECIMAL PLACES and the square root of 4 is 2. Answer E.
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



SVP
Joined: 06 Nov 2014
Posts: 1877

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
30 May 2016, 19:53
(3√0,000064)^(1/2) Or [(0.000064)^(1/3) ]^(1/2)
Start from the inner most value.
0.000064 = 64/1000000 (0.000064)^(1/3) = 4/100 {(0.000064)^(1/3) ]^(1/2) = (4/100)^(1/2) = 2/10
Correct Option: E



Senior Manager
Joined: 18 Jan 2010
Posts: 251

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
30 May 2016, 21:30
Bunuel wrote: 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
We should attempt to write 0.000064 as a cube so that its cube root can be easily taken. 0.000064 = 64 * \(10^{6}\) = \(4^3\) * \(10^{6}\) \sqrt[3]{0.000064} = 4 * \(10^{2}\) = \(2^2\) * Square of (\(10^{1}\)) = 0.2



Manager
Joined: 06 Jun 2014
Posts: 88
Location: United States
Concentration: Finance, General Management
GPA: 3.47

Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
Show Tags
18 Jun 2016, 18:21
Here is another version..
Attachments
qustion.jpg [ 302.81 KiB  Viewed 7018 times ]
_________________
1) Kaplanprep 450 Q27 V21 2) Manhattan 530 Q35 V28 3) GmatPrep 450 Q33, V19 4) Veritas 460 Q31, V23 5) Veritas 440 Q 30, V21 6) Veritas 500 Q34, V 25 7) Gmat 420 Q27, V23 8) Veritas 520 Q36, V26 2/2 9) Veritas 540 Q37, V28 4/19 10)Manhattan 560 Q40, V28 4/28




Re: Which of the following is the value of root{3rd rt{0,000064}
[#permalink]
18 Jun 2016, 18:21



Go to page
1 2
Next
[ 25 posts ]



