Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 02 May 2016, 23:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Which of the following is the value of root{3rd rt{0,000064}

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 32569
Followers: 5642

Kudos [?]: 68470 [1] , given: 9805

Which of the following is the value of root{3rd rt{0,000064} [#permalink]

### Show Tags

30 Jul 2012, 02:02
1
KUDOS
Expert's post
7
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

76% (01:46) correct 24% (00:46) wrong based on 1026 sessions

### HideShow timer Statictics

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
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 32569
Followers: 5642

Kudos [?]: 68470 [3] , given: 9805

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

### Show Tags

30 Jul 2012, 02:02
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
SOLUTION

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)
_________________
Intern
Joined: 27 Jul 2012
Posts: 25
Followers: 0

Kudos [?]: 21 [2] , given: 14

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

### Show Tags

30 Jul 2012, 02:39
2
KUDOS
(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: 71
Location: India
WE: General Management (Energy and Utilities)
Followers: 3

Kudos [?]: 81 [0], given: 15

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

### Show Tags

30 Jul 2012, 03:04
1
This post was
BOOKMARKED
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
Intern
Joined: 17 Jul 2011
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 4

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

### Show Tags

31 Jul 2012, 07:40
Hi,

can you please explain hoe you arrived at

[ 4/10^2]^1/2

Regards
Sanjiv
Math Expert
Joined: 02 Sep 2009
Posts: 32569
Followers: 5642

Kudos [?]: 68470 [0], given: 9805

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

### Show Tags

03 Aug 2012, 04:59
Expert's post
1
This post was
BOOKMARKED
SOLUTION

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)
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 32569
Followers: 5642

Kudos [?]: 68470 [0], given: 9805

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

### Show Tags

05 Jun 2013, 04:28
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on roots problems: math-number-theory-88376.html

All DS roots problems to practice: search.php?search_id=tag&tag_id=49
All PS roots problems to practice: search.php?search_id=tag&tag_id=113

Tough and tricky exponents and roots questions (DS): tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky exponents and roots questions (PS): new-tough-and-tricky-exponents-and-roots-questions-125956.html

_________________
Intern
Joined: 09 Apr 2013
Posts: 32
Location: United States
Concentration: Social Entrepreneurship, Strategy
GMAT 1: 750 Q50 V41
GPA: 3.55
Followers: 1

Kudos [?]: 29 [1] , given: 0

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

### Show Tags

05 Jun 2013, 09:06
1
KUDOS
1
This post was
BOOKMARKED
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

Manager
Joined: 27 Apr 2012
Posts: 62
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
Followers: 1

Kudos [?]: 37 [1] , given: 21

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

### Show Tags

05 Jun 2013, 18:09
1
KUDOS
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: 17
GPA: 3.89
Followers: 1

Kudos [?]: 2 [0], given: 5

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

### Show Tags

02 Feb 2014, 23:19
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?

Math Expert
Joined: 02 Sep 2009
Posts: 32569
Followers: 5642

Kudos [?]: 68470 [0], given: 9805

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

### Show Tags

04 Feb 2014, 02:43
Expert's post
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?

_________________
Senior Manager
Joined: 29 Oct 2013
Posts: 277
Concentration: Finance
Schools: Cornell AMBA'17
GMAT 1: 750 Q V
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 13

Kudos [?]: 294 [0], given: 179

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

### Show Tags

22 May 2014, 12:20
(64/1000000)^1/6={2^(6)/10^(6)}^1/6 = {2^(6*1/6)/10^(6*1/6)}= 2/10= .2
_________________

Please consider giving 'kudos' if you like my post and want to thank

Manager
Joined: 13 Feb 2011
Posts: 104
Followers: 0

Kudos [?]: 19 [0], given: 3344

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

### Show Tags

19 Aug 2014, 17:16
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: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 34

Kudos [?]: 1473 [0], given: 193

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

### Show Tags

19 Aug 2014, 22:04
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

$$\sqrt{\sqrt[3]{0.000064}} = \sqrt[(2*3)]{\frac{64}{10^6}} = (\frac{2^6}{10^6})^{\frac{1}{6}} = \frac{2}{10} = 0.2$$

_________________

Kindly press "+1 Kudos" to appreciate

Current Student
Joined: 08 Feb 2014
Posts: 206
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)
Followers: 2

Kudos [?]: 76 [0], given: 145

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

### Show Tags

09 Dec 2014, 20:26
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
Director
Joined: 10 Mar 2013
Posts: 605
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 8

Kudos [?]: 129 [0], given: 200

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

### Show Tags

27 Apr 2015, 12:39
--> (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.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Manager
Joined: 10 Jul 2015
Posts: 78
GMAT 1: 770 Q47 V48
WE: Education (Education)
Followers: 5

Kudos [?]: 17 [0], given: 12

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

### Show Tags

11 Apr 2016, 16:30
Attached is a visual that should help.
Attachments

Screen Shot 2016-04-11 at 4.29.25 PM.png [ 148.45 KiB | Viewed 283 times ]

Re: Which of the following is the value of root{3rd rt{0,000064}   [#permalink] 11 Apr 2016, 16:30
Similar topics Replies Last post
Similar
Topics:
Which of the following values is the greatest? 3 15 Jan 2015, 08:54
16 Which of the following represents the greatest value? 7 05 Jul 2011, 12:15
18 For which of the following values of x is 15 24 Aug 2010, 12:41
5 For which of the following values of x is 4 21 Mar 2010, 11:00
9 Which of the following has the greatest value? 10 25 Jan 2010, 00:20
Display posts from previous: Sort by